STRUCTURAL    DRAFTING 

AND 

THE  DESIGN   OF   DETAILS 


STRUCTURAL    DRAFTING 

AND 

THE   DESIGN   OF   DETAILS 


BY 

CARLTON  THOMAS  BISHOP,  C.E. 

ASSISTANT    PROFESSOR   OF    STRUCTURAL    ENGINEERING,    SHEFFIELD    SCIENTIFIC    SCHOOL    OF    TALE    UNIVERSITY 
FORMERLY    DRAFTSMAN    FOR   THE    AMERICAN    BRIDGE    COMPANY    AND 
CHIEF    DRAFTSMAN    FOR   THE    HAY    FOUNDRY    AND    IRON   WORKS 


•     •**•«      » 

"     >   ;     ; 

•  •»»*•••  »•)  * 

:'  '  /.  :    ::;v-  '•  •- 
FIRST  EDITION  •»*•»'•»«»  2;    -.- 


NEW  YORK 

JOHN  WILEY  AND  SONS,  INC. 

LONDON:  CHAPMAN  AND  HALL,  LIMITED 

1920 


X 


COPYRIGHT,     IQ20 
BY    CARLTON    T.    BISHOP 


THE • PLIMPTON • PEESS 
NOIWOOO    •    MASS    •   U-S-A 


PREFACE 


THIS  book  has  been  prepared  especially  to  meet  the  requirements  of 
engineering  students,  structural  draftsmen,  and  apprentices  in  structural 
drafting.  It  corresponds  in  scope  to  the  duties  of  the  structural  steel 
draftsmen,  and  it  therefore  covers,  not  only  tli  preparation  of  the  de- 
tailed working  drawings  for  steel  structures,  but  also  the  design  of  the 
details  of  construction.  It  is  a  text-book  j  'tural  Drafting,  and  it 

may  be  used  as  a  text-book  in  elementary  S'niclural  Design.  As  a  refer- 
ence book  for  structural  draftsmen,  it  give  tical  points  as  well  as 
theory.  A  knowledge  of  the  use  of  drawing  instruments  is  presupposed, 
but  the  fundamentals  of  structural  drafting  are  fully  presented.  The 
application  of  these  fundamentals  is  illustrated  by  the  drawings  of  many 
different  types  of  members  of  steel  structure^.  Exceptionally  exhaustive 
are  the  chapters  on  the  design  of  beams  and  the  cc:aponent  parts  of  plate 
girders.  The  tables  at  the  end  of  the  book  are  sufficiently  complete  for 
most  student  courses,  so  that  no  steel  manufacturers'  handbook  need  be 
used.  Many  of  the  tables  are  arranged  more  conveniently  for  both  stu- 
dents and  draftsmen  than  the  tables  in  the  usual  handbooks,  particularly 
the  tables  for  I-beams,  channels,  and  angles.  A  more  complete  outline  of 
the  book  is  given  in  Chapter  I. 

The  illustrative  drawings  have  all  been  prepared  by  the  author,  but 
many  of  them  have  been  adapted  from  similar  or  nearly  identical  draw- 


ings kindly  furnished  by  structural  companies,  to  which  due  acknowledge- 
ment is  here  made.  The  drawings  and  the  standards  of  the  American 
Bridge  Company  have  been  of  exceptional  value,  and  the  drawings  of 
the  King  Bridge  Company,  the  Hay  Foundry  and  Iron  Works,  the  Bos- 
ton Bridge  Works,  the  Mount  Vernon  Bridge  Company,  the  Pennsyl- 
vania Steel  Company,  and  the  Central  Railroad  of  New  Jersey  have 
been  used  to  advantage.  Abstracts  from  the  Specifications  of  the  Ameri- 
can Railway  Engineering  Association  have  been  used  freely  throughout 
the  text  and  in  the  tables  by  permission  of  the  Committee  on  Publica- 
tions of  that  Association. 

Grateful  acknowledgement  is.  made  to  Professor  J.  C.  Tracy,  Head  of 
the  Department  of  Civil  Engineering  at  Yale  University,  and  to  Professor 
J.  R.  Schultz,  Head  of  the  Department  of  English  at  Allegheny  College, 
for  their  helpful  criticisms  of  the  manuscript.  Professor  Tracy  gave  much 
thought  to  the  perusal  of  nine  of  the  most  fundamental  chapters  of  Part 
II,  and  as  a  result  of  his  constructive  criticisms,  these  chapters,  as  well 
as  the  others  in  the  book,  have  been  greatly  improved.  Professor  Schultz 
has  read  the  whole  manuscript  and  has  made  many  valuable  suggestions. 

CARLTON  T.  BISHOP 
NEW  HAVEN,  CONNECTICUT,  September  1919 


A    -4       t    **  f\   s*. 


LIST  OF  CHAPTERS 


PART  I  —  INTRODUCTORY 

CHAPTER  PAOB 

I.   OUTLINE   OF  THE   BOOK  —  NOTATION  —  DEFINITIONS 1 

II.  THE  ORGANIZATION  OF  A  STRUCTURAL  COMPANY  —  THE  ENGINEER- 
ING DEPARTMENT 19 

III.  THE  MANUFACTURE  OP  STRUCTURAL  STEEL 23 

IV.  THE  FABRICATION  OF  STRUCTURAL  STEEL 27 

PART  II  —  STRUCTURAL  DRAFTING 

V.  STRUCTURAL  DRAWINGS  —  THE  DRAWING 33 

VI.   STRUCTURAL      DRAWINGS  —  THE     CONVENTIONAL     METHODS     OF 

REPRESENTATION 37 

VII.   STRUCTURAL      DRAWINGS  —  THE     CONVENTIONAL     METHODS     OF 

BILLING 43 

VIII.   STRUCTURAL  DRAWINGS  —  THE  DIMENSIONS 46 

IX.  STRUCTURAL  DRAWINGS  —  THE  NOTES,  THE  TITLE,  AND  THE  BORDER      52 

X.   INKING  AND  TRACING 55 

XI.   ERASING 62 

XII.   DRAWING  DIRECTLY  IN  INK  ON  TRACING  CLOTH 65 

XIII.  RIVET  SPACING 68 

XIV.  CLEARANCE,  AND  ERECTION  CONSIDERATIONS 72 

XV.  LAYOUTS 75 

XVI.   MARKING  SYSTEMS 79 

XVII.  BEAMS 83 

XVIII.   PLATE  GIRDERS 95 

XIX.   LATTICED  GIRDERS 108 

XX.  ROOF  TRUSSES 113 

XXI.  BRIDGE  TRUSSES  .  .  120 


CHAPTER  PAOB 

XXII.  COLUMNS 131 

XXIII.  BRACING  SYSTEMS 138 

XXIV.  MISCELLANEOUS  FRAMING 146 

XXV.   ERECTION  PLANS  AND  DIAGRAMS 151 

XXVI.   MATERIAL  ORDER  BILLS 162 

XXVII.   SHOP  BILLS  AND  SHIPPING  BILLS 167 

XXVIII.   MISCELLANEOUS  DRAWINGS  AND  LISTS 174 

XXIX.   CHECKING  AND  CORRECTING  DRAWINGS 179 

PART  III  — THE  DESIGN   OF   DETAILS 

XXX.   SHEAR  AND  BENDING  MOMENT '. 183 

XXXI.  THE  DESIGN  OF  BEAMS 197 

XXXII.   THE  DESIGN  OF  TENSION  AND  COMPRESSION  MEMBERS 206 

XXXIII.  THE  DESIGN  OF  PLATE  GIRDERS 218 

XXXIV.  THE  THEORY  AND  PRACTICE  OF  RIVETING 228 

XXXV.   RIVETS  IN  TYPICAL  CONNECTIONS 233 

XXXVI.  RIVETS  IN  ECCENTRIC  CONNECTIONS 237 

XXXVII.   RIVETS  IN  THE  FLANGES  OF  PLATE  GIRDERS 241 

XXXVIII.  COVER  PLATES 259 

XXXIX.   WEB  STIFFENERS 266 

XL.   SPLICES 270 

XLI.   PINS 278 

XLII.   REINFORCING  PLATES 284 

XLIII.   BEARING  PLATES  AND  COLUMN  BASES 288 

XLIV.   GRILLAGE  BEAMS 291 

TABLES  AND  DIAGRAMS 297 

DESCRIPTION  OF  TABLES  AND  DIAGRAMS 334 

INDEX..                                                                                                339 


Vll 


TABLE  OF  CONTENTS 


PART   I  —  INTRODUCTORY 

CHAPTER  I 
OUTLINE   OF   THE   BOOK  —  NOTATION  —  DEFINITIONS  PAGE 

Scope  —  The  general  arrangement  —  Outline  of  a  course  of  study  —  Num- 
bering —  Cross  references  —  Type  —  Formulas  —  Notation  —  Definitions  of 
engineering  terma 1 

CHAPTER  II 

THE   ORGANIZATION    OF   A   STRUCTURAL   COMPANY  —  THE 
ENGINEERING   DEPARTMENT 

The  structural  draftsman  —  The  Estimating  or  Designing  Department  —  The 
Drafting  Department  —  The  templet  shop  —  The  manufacture  of  steel  — 
The  structural  shop  —  Erection  —  The  Engineering  Department  —  The 
Designing  Department  —  Design  sheets  • —  The  Drafting  Department  — 
Method  of  procedure  —  Progress  sheets  —  Cooperation 19 

CHAPTER  III 

THE   MANUFACTURE   OF   STRUCTURAL   STEEL 
Iron  —  Structural  steel  —  Rolling  the  steel  —  The  effect  of  spreading  the  rolls  — 

Mill  variation  —  Plates  —  The  actual  shapes 23 

CHAPTER  IV 
THE   FABRICATION    OF   STRUCTURAL  STEEL 

Fabrication  — •  Elementary  points  —  Shop  methods  —  The  plant  layout  —  The 
templet  shop  —  The  stock  yard  —  Shearing  —  Straightening  rolls  —  Laying 
out  —  Coping  —  Other  preliminary  operations  —  Punching  —  Drilling  — 
Sub-punching  —  Assembling  —  Riveting  —  Milling  —  Boring  —  Inspection  — 
Painting  —  Shipping  —  Other  operations 27 

PART   II  —  STRUCTURAL   DRAFTING 

CHAPTER  V 

STRUCTURAL   DRAWINGS  — THE   DRAWING 

A  structural  drawing  — -  Elements  —  Projection  —  The  proper  views  —  Top 
view  —  Front  view  —  End  view  —  Bottom  sectional  view  —  Sectional  view 


—  The  distances  between  views  —  The  position  on  the  sheet  —  Parts  shown  — 
Symmetrical  members  —  The  usual  working  units  —  A  preliminary  freehand 
sketch  —  Too  accurate  plotting  —  The  scale  —  The  size  of  the  drawings  — 

—  Drawings  made   on  paper  or   tracing   cloth  —  Black  waterproof   India 
ink  —  Systematic  method  of  procedure  —  A  draftsman  should  always  check 

his  own  work '. 33 

CHAPTER  VI 

STRUCTURAL  DRAWINGS  — THE   CONVENTIONAL  METHODS 
OF   REPRESENTATION 

The  lines  of  a  drawing  —  Sectional  views  —  Breaks  —  Curved  surfaces  —  Con- 
ventional representation  — •  The  shapes  most  used  —  A  plate  —  An  angle  — 
An  I-beam  —  A  channel  —  Round  and  square  rods  —  A  tee  —  A  Z-bar  —  A 
rail  —  An  eye  bar  —  Lattice  bars  —  Shop  rivets  and  holes  for  field  rivets  — 
All  holes  are  shown  —  Bolts  —  Fillers  —  Bent  plates  —  Other  materials ....  37 

CHAPTER  VII 
STRUCTURAL  DRAWINGS  — THE  CONVENTIONAL  METHODS  OF  BILLING 

Billing  —  Conventional  signs  —  Plates  —  Angles  —  I-beams  —  Channels  —  Rods 

—  Tees  —  Z-bars  —  Rails  —  Eye  bars  —  Lattice  bars  —  Washers  —  Rivets 

—  Bolts  — :  Holes  —  Special  abbreviations 43 

CHAPTER  VIII 

STRUCTURAL  DRAWINGS —THE  DIMENSIONS 

Dimension  and  size  —  The  dimensions  —  Actual  measurements  —  Placed  upon 
the  drawing  as  soon  as  determined  —  Position  —  Dimension  lines  —  Placed 
outside  of  the  view  —  Space  between  dimension  lines  —  Arrow  heads  — 
Dimension  figures  —  Placed  above  the  dimension  lines  —  Fractions  —  Mis- 
takes — When  the  space  between  arrow  heads  is  limited  —  Figures  and  notes 
read  from  the  bottom  edge  or  from  the  right-hand  edge  —  Feet  and  inches — 
Decimals  —  Method  of  writing  dimension  figures  —  Recurring  dimensions 

—  A  dimension  should  not  be  repeated  — Rivets  and  holes  —  Staggered  rivets 

—  The  gages  —  Edge  distances  —  A  line  of  rivet  spacing  —  Edges  of  the 
flanges  —  Spaces  dimensioned  in  a  group  —  Supplementary  dimension  line 


X 


TABLE  OF  CONTENTS 


CHAPTER  VIII — Continued 
STRUCTURAL  DRAWINGS— THE  DIMENSIONS  —  Continued 

PAGE 

—  The  sum  of  the  dimensions  —  Shopmen  should  not  be  compelled  to  add 
or  subtract  —  One  method  of  dimensioning  —  Field  connections  —  Lattice 
bars  —  The  slope  of  a  line 46 

CHAPTER  IX 

STRUCTURAL  DRAWINGS  —  THE   NOTES,   THE  TITLE, 
AND   THE   BORDER 

The  notes  —  General  notes  —  Other  notes  —  Rivets  and  holes  —  Identification 
mark  —  Number  of  pieces  —  Reference  to  other  drawings  —  Loose  pieces 
bolted  —  Permanent  bolts  —  Different  members  combined  —  All  notes 
should  be  made  positive  —  The  title  placed  in  the  lower  right-hand  corner 

—  The  first  part  —  The  second  part  —  The  smaller  drawings  —  Sheet  num- 
bers —  The  border 52 

CHAPTER  X 

INKING  AND   TRACING 

Structural  drawings  —  Three  methods  of  making  drawings —  The  care  of  tracing 
cloth  —  The  dull  or  unglazed  side  —  The  selvage  edges  —  Cloth  tightly 
stretched  —  The  surface  of  the  cloth  —  A  good  ruling  pen  —  Pen  in  good  con- 
dition —  The  compasses  —  The  lettering  pen  —  Black  ink  —  Red  ink  — 
Should  never  be  shaken  —  Frozen  ink  —  The  straight-edge  —  Drawing  too 
close  to  the  straight-edge  —  An  easy  posture  —  A  continuous  stroke  • —  One 
setting  of  the  pen  — -  Stopping  the  pen  —  Lines  drawn  away  from  intersec- 
tions —  Heavy  lines  —  Parallel  lines  —  Curves  —  Need  not  wait  for  ink  to 
dry  —  Rush  work  —  A  blotter  should  not  be  used  —  Systematic  method  of 
procedure  —  Fine  lines  —  Heavier  main  lines  —  Rivets  and  holes  —  Arrow 
heads  —  Dimension  figures  —  Billing  material  —  List  of  members  —  Notes 

—  Title  —  Border  —  Tracing  should  be  inverted 55 

CHAPTER  XI 

ERASING 

To  erase  properly  —  The  object  of  erasing  —  Erase  willingly  —  Guard  against 
mistakes  —  The  secret  of  erasing  —  The  eraser  —  Ink  eradicator  —  A  knife  or 
metal  scratcher  should  not  be  used  —  An  erasing  shield  —  A  brush  —  The 
surface  of  the  cloth  —  Replace  lines  and  figures  erased  by  mistake  —  Pencil 
lines 62 

CHAPTER  XII 
DRAWING  DIRECTLY  IN  INK   ON  TRACING   CLOTH 

Method  recommended  —  Tracers  —  Arguments  —  Not  all  drawings  are  well 
adapted  to  this  method  —  A  drawing  must  be  carefully  planned  —  Paper 
placed  underneath  the  cloth  —  Illustration 65 


CHAPTER  XIII 
RIVET   SPACING 

PAGE 

Rivet  spacing  —  Rivet  pitch  —  General  rules  —  Set  of  standards  —  The  specifica- 
tions —  Standard  gages  —  The  minimum  spacing  —  The  maximum  spacing 

—  Wide   cover   plates  —  Edge   distance  —  Stitch    rivets  —  Lattice   bars  — 
Practical  points  —  Usual  spaces  —  Continuous  rivet  spacing 08 

CHAPTER  XIV 
CLEARANCE,   AND   ERECTION   CONSIDERATIONS 

Clearance  —  Provision  for  overrun  —  Tight  fits  —  Projecting  parts  —  Erection 
clearance  —  Seat  angles  —  Holes  for  anchor  bolts  —  Other  connections  — 
Driving  clearance  —  Other  erection  considerations 72 

CHAPTER  XV 
LAYOUTS 

A  layout  —  When  used  —  A  simple  layout  —  Three  common  types  —  Method 
of  procedure  for  a  gusset  plate  —  The  calculation  of  the  slope  —  Lateral 
plates  —  Bent-plate  work 

CHAPTER  XVI 
MARKING   SYSTEMS 

Two  kinds  of  marks  —  Assembling  marks  — When  used  — Three  parts  — The 
first  letter  —  The  second  letter  —  The  sheet  number  —  Rights  and  lefts  — 
Summary  —  Shipping    marks  —  Two    parts  —  Marked    conspicuously  — 
Rights  and  lefts  —  Members  combined  —  Opposites  —  Office-building  con- 
struction —  Bridge  trusses  —  Roof  trusses  —  Tie  rods  —  Direction  marks ...     79 

CHAPTER  XVII 
BEAMS 

A  simple  beam  —  A  cantilever  beam  —  A  continuous  beam  —  Made  of  a  single 
main  piece  —  I-beam  and  channel  —  Printed  forms  —  Beams  are  supported 

—  Standard  connection  angles  —  Three  different  methods  —  The  modified 
method  —  Single  angles  —  Different  depths  —  Standard  angles  are  designed 

—  Beams  shown  full  length  —  Web  connections  located  horizontally  in  two 
ways  —  The  length  of  a  beam  —  Ordered  length  —  Mill  variation  —  Bearing 
plates  —  Coping  —  Office-building  construction  —  Purlins  —  Tie  rods  —  Sag 
rods  —  Multiple  beam  punch  —  Nailing  strips  or  spiking  pieces—  Holes  in  the 
flanges  —  Beam  girders  —  Box  sections  —  Wall  plates  —  Skewback  angles- 
Crane  runway  beams  —  Skew  connections 83 


TABLE  OF  CONTENTS 


XI 


CHAPTER  XVIII 
PLATE   GIRDERS 

PAGE 

Adaptability  —  Types  —  Main  dimensions  —  End  stiffening  angles  —  Flange 
angles  —  Web  plates  —  Intermediate  stiffening  angles  —  Fillers  —  Crimped 
stiffeners  —  Cover  plates  —  Flange  rivets  —  Rivets  in  cover  plates  —  Gages 

—  Rivets  in  outstanding  legs  —  Holes  for  anchor  bolts  —  Reference  dimen- 
sions —  Reference  line  —  Box  girder  —  Camber  —  Curved  ends 95 

CHAPTER  XIX 
LATTICED   GIRDERS 

Definition  —  Common  form  —  End  connections  —  Proportions  —  Working  lines 

—  Panel    depth  —  Panel    length  —  Dimensions  —  Plates  —  Different    num- 
bers of  rivets  in  diagonals  —  End  connection  plates  —  Double  latticed  girders 

—  Stitch  rivets  —  Typical  connections  —  Stiffening  girder 108 

CHAPTER  XX 
ROOF  TRUSSES 

Steel  roof  trusses  —  Common  types  —  The  pitch  —  Purlin  spacing  —  Form  of 
support  —  Arrangement  on  the  sheet  —  System  of  working  lines  —  Form  of 
members  —  Gusset  plates  —  Stitch  rivets  —  Center  hanger  —  Shipment  — 

—  Ridge  strut  —  Purlin   connections  —  Bracing  rods  — Bottom-chord  brac- 
ing —  Future  extension  —  Gable  end  —  Louvres 113 

CHAPTER  XXI 
BRIDGE   TRUSSES 

When  used  —  Common  types  —  The  joints  —  Arrangement  on  the  sheet  —  Ar- 
rangement of  views  —  Shipping  marks  —  Camber  —  Size  of  pin  holes  — 
Types  of  members  —  Milling  —  Splices  —  Reinforcing  plates  —  Counter- 
sunk or  flattened  rivets  —  Protection  from  the  weather  —  Clearance  — 
Method  of  holding  a  counter 120 

CHAPTER  XXII 
COLUMNS 

Steel  columns  —  Position  on  the  sheet  —  Different  types  of  columns  —  Plate  and 
channel  columns  —  The  important  dimension  —  Beam  connections  —  Sec- 
tional views  —  Typical  mill-building  column  —  Connections  —  Column  base 

—  Milling  —  Vertical      dimensions  —  Gages  —  Gable      column  —  Latticed 
columns 131 


CHAPTER  XXIII 
BRACING   SYSTEMS 

Bracing  —  Considered  as  trusses  —  Statically  complete  —  The  lines  of  stress  — 
Arrangement  —  Initial  tension  —  Connections  —  Gages  —  Illustrations  — 
Mill-building  bracing  —  Bottom-chord  bracing  —  Unsymmetrical  bracing  — 
Knee  braces  —  Bottom  lateral  bracing  —  Top  lateral  system  —  Brackets  — 
Cross  Frames  —  Office-building  bracing 


138 


CHAPTER  XXIV 
MISCELLANEOUS  FRAMING 

Illustrative  drawings  —  Girts  —  Struts  —  Plate  work  —  Skew  work  —  Miscel- 
laneous material 146 

CHAPTER  XXV 
ERECTION  PLANS  AND  DIAGRAMS 

The  plans  and  diagrams  —  The  draftsman  —  The  erector  —  Other  contractors  — 
Typical  plans  and  diagrams  —  Plate  girder  bridges  —  Truss  bridge  — 
Anchor-bolt  plan  —  Erection  diagram  for  a  mill  building  —  Crane  clearance 
diagram  —  Corrugated  steel  —  Floor  plan  of  an  office  building  —  Method  of 
procedure  —  Different  floors  —  Column  schedule  —  Record  of  Drawings  — 
Progress  record  for  beam  drawings  —  Progress  record  for  columns 151 

CHAPTER  XXVI 
MATERIAL  ORDER  BILLS 

Purpose  —  Lists  of  material  —  Methods  —  Miscellaneous  material  —  Two  parts 

—  Drawings  conform  to  the  material  ordered  —  The  arrangement  —  Ship- 
ments —  Numbering  —  Specifications  —  Shipping  direct  to  site  —  Changes 

—  Ordered  lengths  —  Beams  —  Angles  —  Plates  —  Lattice  bars  —  Tie  rods 

—  Sag  rods  —  Gas  pipe  —  Rails 162 

CHAPTER  XXVII 
SHOP  BILLS  AND   SHIPPING  BILLS 

A  shop  bill  —  Form  —  Numbering  —  Three  parts  —  Arrangement  —  Itemizing  — 
.Item  number  —  Number  of  pieces  —  Section  —  Length  —  Calculated  weight 

—  A  shipping  bill  —  Shop  and  shipping  bills  combined  —  Combination  sheets     167 

CHAPTER  XXVIII 
MISCELLANEOUS  DRAWINGS   AND   LISTS 

Miscellaneous  material  —  Special  printed  forms  —  Cast-iron  base  —  Rods  — 
Field  rivets  and  bolts  —  Erector's  list  —  Summary  of  field  rivets  and  bolts  — 
Erection  bolts .  .  174 


Xll 


TABLE  OF  CONTENTS 


CHAPTER  XXIX 

CHECKING   AND   CORRECTING   DRAWINGS  PAGE 

A  checker  —  Not  all  drawings  are  completely  checked  —  A  detailer  should  be 
familiar  with  the  method  of  checking  —  A  checker  should  work  systematically 

—  Suggestions  —  Indicating  mistakes  —  Check  marks  —  Back-checking  — 
Students'  drawings  —  Corrections  —  Revisions 179 

PAKT  III  — THE  DESIGN   OF  DETAILS 

CHAPTER  XXX 
SHEAR   AND   BENDING   MOMENT 

The  terms  —  Principles  —  Signs  —  Forces  considered  —  Shear  —  Bending  mo- 
ment —  Formulas  —  Sketches  —  Arrangement  —  Reactions  —  Concentrated 
Loads  —  Uniformly  distributed  loads  —  Combined  loads  —  Short-cut  rule 

—  Relation  between  shear  and  bending  moment  —  Live  loads  —  Impact  — 
Live-load  shear,  simple  and  cantilever  beams  —  Live-load  bending  moment, 
simple  and  cantilever  beams,  concentrated,  uniformly  distributed,  and  com- 
bined loads  —  Restrained  beams  —  Continuous  beams  —  Conventional  wheel- 
load  systems  —  Maximum  shear  on  beam  —  Maximum  shear  for  any  section 

—  Maximum  floor-beam  reaction  —  Absolute  maximum  bending  moment  — 
Maximum  bending  moment  at  any  point  —  Through  girders  —  Trusses ....     183 

CHAPTER  XXXI 
THE  DESIGN   OF  BEAMS 

General  —  Points     considered  —  Effects     of     bending  —  Resisting     Moment  — 
Theory  —  Unit  stress  -*-  Section  modulus  —  Units  —  Rectangular  beams  — 
Cylindrical  beams  —  Steel  beams  —  Beams  must  be  self-supporting  —  A  beam 
is  weakened  by  holes  —  Lateral  supports  —  Lateral  thrust  —  Shear  —  Bear- 
ing —  Deflection 197 

CHAPTER  XXXII 

THE  DESIGN   OF   TENSION   AND   COMPRESSION   MEMBERS 
Practical  points  —  A  tension  member  —  A  compression  member  —  The  area  of 
cross  section  —  The  form  of  cross  section  —  Effect  of  rivet  holes  —  Weakest 
point  of  a  tension  member  —  Loop  rod  —  Clevis  —  Round  rod  —  Eye  bars 

—  Riveted  tension  members  —  Net  area  of  cross  section  —  The  design  — • 
The  least  net  section  is  not  necessarily  a  right  section  —  Working  rule  for 
effective  net  section  —  Smaller  net  section  near  the  ends  —  Compression 
members  —  Strength  —  Compression  formula  —  The  radius  of  gyration  — 
The  moment  of  inertia  —  The  forms  of  members  —  Members  which  resist 
bending  and  direct  stress  —  Lattice  bars  and  tie  plates  —  The  design  —  A 

tie  plate  —  Lattice  bars  —  Method  of  design 206 

CHAPTER  XXXIII 

THE   DESIGN   OF   PLATE   GIRDERS 
The  common  forms  —  Analysis  of  forces  —  The  depth  —  The  web  plate  —  The 


flanges  —  Flange  angles —  Cover  plates  —  Distribution  of  area  —  The  com- 
pression flange  —  Three  methods  of  design  —  The  degree  of  accuracy  —  Case 
A  —  Assumptions  —  Theory  —  Case  B  —  Assumptions  —  Two  more  steps 

—  Theory  —  The  effective  depth  —  Lateral  forces  —  Vertical  flange  plates  — 
Centrifugal  forces 218 

CHAPTER  XXXIV 
THE   THEORY  AND   PRACTICE   OF   RIVETING 

Rivets  —  Shop  and  field  rivets  —  Position  in  member  —  Assumptions  —  The 
design  of  a  riveted  joint  —  Nominal  diameter  —  The  strength  of  a  rivet  in 
shear  —  Single  shear  —  Double  shear  —  The  strength  of  a  rivet  in  bearing  — 
Bolts  —  Number  of  rivets  required  —  Flattened  and  countersunk  rivets  — 
Indirect  riveting  —  Typical  riveted  connections 228 

CHAPTER  XXXV 

RIVETS   IN   TYPICAL   CONNECTIONS 

Typical  riveted  connections  —  Gusset  plates,  continuous  and  spliced  chords  — 
Symmetrical  gusset  plates  —  Web  connection  for  beams  —  Seat  connection  for 
beams  —  Stringer  connection  —  Floor-beam  connection  —  Other  connections  233 

CHAPTER  XXXVI 

RIVETS   IN   ECCENTRIC   CONNECTIONS 
Definition  —  Method  of  designing  —  Theory  —  Working  rule 

CHAPTER  XXXVII 
RIVETS   IN   THE   FLANGES   OF   PLATE   GIRDERS 

Flange  rivets  —  Rivet  pitch  —  Inclined  girders  —  Complete  treatise  —  General 
discussion  —  Controlling  factors  —  Forces  considered  —  Depth  —  Different 
cases  —  Case  I,  Concentrated  static  loads  applied  to  the  web  —  How  applied 

—  Bending  moment  theory  —  Shear  theory  —  Case  II,  Uniformly  distributed 
static  loads  applied  to  the  web  —  How  applied  —  Theory  —  Case  III,  Com- 
bined concentrated  and  uniformly  distributed  loads  applied  to  the  web  — 
Method  —  Variable  fixed  loads  —  Case  IV,  Moving  loads  applied  to  the  web 

—  How  applied  —  Theory  —  Approximate  method  —  Case  V,  Loads  applied 
to   the  flange  — How  applied  —  Theory  —  Loads   applied   to   the   bottom 
flange  —  Case  VI,  Girders  in  which  the  web  is  considered  to  resist  part  of  the 
stress  due  to  bending  moment  —  Method  —  Case  VII,  Box  girders,  cantilever 
girders,  and  girders  with  non-parallel  flanges  —  A  box  girder  —  A  cantilever 
girder  —  Girders  with  non-parallel  flanges  —  Case  VIII,  Girders  with  vertical 
flange  plates,  and  girders  with  four  angles  in  each  flange — When  used  — 
Vertical  flange  plates  —  Theory  —  Four  angles  in  each  flange  —  The  de- 
termination of  the  minimum  pitch  based  upon  the  strength  of  the  web  — 
Importance  —  A   table   of   minimum   pitches  —  Unit    stresses  —  Theory  - 
Summary 


TABLE  OF  CONTENTS 


CHAPTER  XXXVIII 

COVER  PLATES  PAGE 

Use  —  Some  cover  plates  extend  the  full  length  —  The  theoretical  length  —  The 
graphic  method  —  The  algebraic  method  —  Symmetrical  loads  —  Uniformly 
distributed  loads  —  Concentrated  loads  —  Variable  concentrated  loads  — 
Moving  concentrated  loads  —  Algebraic  method  —  Rivets  in  cover  plates  — 
Four  points  considered  —  Increase  in  flange  stress  —  Each  plate  should  be 

developed  by  rivets 259 

CHAPTER  XXXIX 
WEB   STIFFENERS 

Shearing  stresses  —  Vertical  stiffening  angles  or  stiffeners  —  The  thickness  of  the 
web  plate  —  End  stiffening  angles  —  Designed  for  bearing  —  The  strength 
in  compression  —  Rivets  —  Intermediate  stiffeners  —  Spacing  —  Rivets  — 
Crimping 266 

CHAPTER  XL 

SPLICES 

Definition  —  Design  —  Three  types  —  Web  splices  —  When  used  —  The  design 
—  Design  for  shear  only  —  Design  for  bending  moment  as  well  as  for  shear  — 
Separate  splice  plates  —  Flange  splices  —  When  used  —  Component  parts  not 
spliced  at  same  point  —  Cover-plate  splice  —  Flange-angle  splice  —  Splice  at 
the  curved  end  of  a  girder  —  Field  splice  in  girder  flange  —  Column  splices  — 

Mill-building  columns  —  Office-building  columns  —  Channel  columns 270 

CHAPTER  XLI 

PINS 

Description  —  Pins  are  designed  as  cylindrical  beams  —  Application  of  forces  — 
Design  for  bending  —  Investigation  for  shear  —  Not  every  pin  in  a  truss  need 
be  designed  —  Packing  —  Horizontal  and  vertical  componenets  —  The  forces 

which  act  —  Computation 278 

CHAPTER  XLII 
REINFORCING   PLATES 

When   used  —  Type   of   member  —  Method  of  design  —  Design  for  bearing  — 
The  number  of  rivets  —  Design     for    tension  —  The   rivets  in    a   tension 
member 284 

CHAPTER  XLIII 

BEARING   PLATES   AND   COLUMN   BASES 
Type  —  Size  of  bearing  plate  —  The  thickness  of  bearing  plate  —  Expansion  — 

Pedestals  and  shoes  —  Column  bases 288 


CHAPTER  XLJV 
GRILLAGE   BEAMS 

When  used  —  Arrangement  —  Tie  rods  —  The  loads  —  The  allowed  bearing  pres- 
sure —  Concrete  mat  —  Method  of  design  —  Design  for  bending  —  Investi- 
gation for  buckling  —  Investigation  for  shear 


TABLES  AND   DIAGRAMS 

Weights  and  dimensions  of  Carnegie  I-beams,  American  Bridge  Company  con- 
nection angles  —  Weights  and  dimensions  of  standard  I-beams,  Lacku  wanna 
connection  angles  —  Weights  and  dimensions  of  Carnegie  Channels,  American 
Bridge  Company  connection  angles  —  Weights  and  dimensions  of  st-mdard 
channels,  Lackawanria  connection  angles  —  Weights  and  dimensiu; 
Bethlehem  I-beams  and  girder  beams,  Bethlehem  connection  angles  — 
Weights  and  areas  of  standard  and  special  angles  —  Gages  of  angles  — 
Areas  of  holes  —  Weights  and  dimensions  of  rivets  and  bolts  —  Rivet  code  - 
Clearance  for  machine-driven  rivets  —  Minimum  rivet  stagger  — •  Minimum 
rivet  spacing  —  Maximum  rivet  spacing  —  Edge  distances  —  Minimum  rivet 
stagger  —  Minimum  pitches  for  flange  rivets  —  Multiplication  table  for  rivet 
spacing  —  Tables  of  rivet  values  —  Charts  for  determining  resultants  graphi- 
cally in  decimals,  inches  and  fractions,  and  feet  and  inches  —  Purlin  con- 
nections —  Lattice  bars  —  Areas  and  weights  of  rods  —  Bearing  plates  — 
Separators  —  Anchors  —  Rod  connections  —  Dimensions  and  properties  of 
rails  —  Rail  fastenings  —  Unit  stresses  for  structural  steel  —  Shear  and 
moment  table  for  Cooper's  engine  loading  —  Properties  of  wooden  rectangular 
beams  —  Unit  stresses  for  structural  timber  —  Moments  of  inertia  of  rec- 
tangles—  Areas  of  plates  —  Weights  of  plates  —  Properties  of  I-bfv.in," - 
Properties  of  channels  —  Properties  of  Bethlehem  I-beams  and  girder  beaoia 
—  List  of  shipping  marks  —  Properties  of  standard  and  special  aiigl-.s  • - 
Net  areas  and  tensile  strengths  of  two-angle  members  —  Unit  stresses  for 
compression  —  Radii  of  gyration  of  two-angle  struts  —  Safe  loads  of  single- 
angle  and  two-angle  struts  —  Table  of  squares  —  Resisting  moments  of  pins  — 
Decimal  equivalents 


DESCRIPTION  OF  TABLES  AND  DIAGRAMS  . . 


INDEX 


STRUCTURAL   DRAFTING 


ND 


THE  DESIGN  OF  DETAILS 


PART  I  —  INTRODUCTORY 


CHAPTER  I 
OUTLINE  OF  THE  BOOK  —  NOTATION  —  DEFINITIONS 

SYNOPSIS:  In  this  chapter  are  summarized  the  arrangement,  the  notation,  and  the 
special  features  of  this  book.  Brief  definitions  are  given  to  show  the  meanings  of  the 
engineering  terms  used  in  the  text. 


1.  Scope.  —  This  book  is  planned  to  meet  the  requirements  of  en- 
gineering students,  of  apprentices,  and  of  structural  draftsmen.  In 
scope  it  is  designed  primarily  to  correspond  to  the  duties  of  the  struc- 
tural draftsman.  It  is  divided  into  three  parts,  emphasis  being  laid 
upon  Part  II  —  Structural  Drafting.  This  Part  II  includes  the  funda- 
mentals of  structural  drafting,  such  as  the  methods  of  representation, 
of  billing,  and  of  dimensioning.  The  application  of  these  fundamentals 
to  the  drawings  of  common  types  of  members  is  fully  illustrated.  In 
Part  III  the  elements  of  design  are  shown  with  special  reference  to  the 
design  of  details  and  of  simple  members  with  which  the  draftsman  must 
be  familiar.  The  design  of  other  members  and  of  complete  structures 
is  omitted  for  two  reasons,  (1)  because  they  are  usually  designed  in  a 
special  Designing  Department  instead  of  in  the  Drafting  Room,  and 
(2)  because  nearly  all  phases  of  structural  design  are  admirably  de- 
scribed in  so  many  books  that  it  would  be  futile  to  duplicate  them  here. 
Part  I  is  introductory  and  is  inserted  primarily  to  give  the  student  a 
conception  of  the  relation  between  the  drafting  room  and  the  other 
branches  of  the  steel  industry.  Tables  are  inserted  at  the  end  of  the 


book.  These  tables  may  supplant  the  handbooks  of  structural  steel 
companies  in  some  student  courses.  The  tables  are  arranged  to  mini- 
mize the  turning  of  pages  when  used  either  in  drawing  or  in  designing. 
This  is  accomplished  by  placing  on  one  page  the  data  usually  given  on 
several  pages.  For  instance,  by  separating  standard  angles  from  special 
angles  the  properties  of  each  may  be  shown  on  a  single  page.  Further- 
more, the  weights  and  areas  of  all  angles  are  grouped  with  the  gages  of 
the  angles  and  the  areas  of  holes,  an  arrangement  which  is  equally 
convenient  for  the  draftsman  when  drawing  and  when  designing.  The 
scope  and  the  use  of  the  tables  may  be  seen  best  by  reference  to  the 
tables  themselves  and  to  the  brief  descriptions  which  follow  them. 

2.  The  general  arrangement  of  the  book  is  planned  for  convenient 
reference.  It  is  believed  that  the  text  will  be  used  chiefly  for  reference 
by  students,  apprentices,  and  draftsmen.  The  shape  of  the  book  is 
such  that  it  will  stay  open  on  the  desk  without  the  use  of  weights  or 
clamps.  The  size  of  the  pages  was  selected  so  that  the  drawings  and 
the  tables  could  be  made  reasonably  large  and  clear  without  the  use  of 
intolerable  folded  inset  sheets. 


PART  I  —  INTRODUCTORY 


1.  The  author  first  planned  a  chapter  which  would  give  an  outline 
o£  a-  .course  .of;  study.  It  was  felt  that  such  an  outline  would  simplify 
thViCssignmerili'  of  'student  work,  and  that  it  would  be  useful  to  appren- 


md'^iSrs  Iwho  might  use  the  book  without  instruction.  It  might 
'also'  Be"  of  service'  to  the  younger  instructors  when  planning  to  use  the 
text  for  the  first  time.  However,  it  was  concluded  that  the  large  major- 
ity of  readers  would  have  no  use  for  such  a  chapter.  Each  instructor 
should  become  familiar  with  the  book  before  he  adopts  it  as  a  text,  and 
he  should  have  little  difficulty  in  selecting  the  proper  sequence  of  para- 
graphs in  the  fundamental  chapters  of  Part  II.  The  author  does  not 
feel  that  it  is  wise  for  the  student  to  devote  much  time  to  a  study  of 
the  text  before  he  begins  to  draw.  The  first  drawing,  if  sufficiently 
simple,  may  be  started  at  the  first  exercise,  accompanied  by  references 
to  the  most  important  paragraphs  that  bear  upon  the  drawing.  This 
may  be  followed  by  other  drawings  each  of  which  illustrates  as  many 
new  points  as  the  average  student  can  master.  The  work  should  be 
progressive,  but  no  drawing  should  involve  points  beyond  the  student's 
ability  and  he  should  be  expected  to  make  each  drawing  fundamentally 
correct.  It  may  be  difficult  to  obtain  excellent  results  at  the  outset 
owing  to  the  multiplicity  of  conventions  and  practical  points  which  are 
new  to  most  students;  but  to  allow  violations  of  drafting  methods  and 
conventions  to  stand  uncorrected  is  a  source  of  trouble.  Reasonable 
requirements  should  be  made  and  enforced,  and  all  mistakes  should  be 
corrected  by  the  students  as  a  safeguard  against  repetition.  It  is  rec- 
ommended that  many  of  the  penciled  drawings  be  left  uninked  in  order 
to  facilitate  the  making  of  changes  and  to  enable  the  students  to  make 
more  drawings  within  the  allotted  time.  The  author  has  found  it 
satisfactory  to  use  printed  forms  for  beam  work  at  the  beginning  of  the 
course,  for  they  not  only  conform  to  the  usual  drafting  room  practice 
but  they  enable  the  student  to  concentrate  his  mind  on  points  other 
than  the  arrangement  of  views  and  of  dimensions  lines  which  he  can 
learn  gradually.  In  order  to  introduce  the  fundamentals  as  early  in 
the  course  as  possible  it  is  expedient  to  have  the  students  make  free- 
hand drawings  at  their  desks  or  at  the  blackboard  instead  of  taking 
time  for  careful  plotting.  As  soon  as  possible  the  data  and  suggestions 
given  with  each  new  problem  should  be  reduced  to  a  minimum  in  order 


to  develop  the  student's  resourcefulness.  Frequent  tests  may  be  given, 
and  one  question  on  each  test  may  well  be  devoted  to  the  indication  of 
mistakes  on  a  given  drawing,  i.e.,  practice  in  checking. 

2.  Numbering.  —  In  this  book  all  pages  are  numbered  consecutively. 
Each  figure  bears  the  same  number  as  the  page  upon  which  it  may  be 
found.     This  facilitates  the  finding  of  any  figure  to  which  reference  is 
made.     When  more  than  one  figure  is  placed  upon  the  same  page  they 
are  lettered,  thus:    Fig.  24  (a)   and  Fig.  24  (6)   are  both  on  page  24. 
The  paragraphs  are  numbered  on  each  page  independently,  beginning 
with  1.     This  is  done  to  avoid  large  paragraph  numbers. 

3.  Cross  references  should  be  made  to  both  the  page  and  the  para- 
graph.    Reference  to  a  page  alone  is  not  sufficiently  specific,  particu- 
larly where  the  paragraphs  are  short  as  in  the  fundamental  chapters  of 
Part  II;    reference  to  a  paragraph  without  the  page  often  results  in  an 
extended  search  because  the  paragraphs  are  of  unequal  lengths  and  on 
some  pages  no  paragraph  number  is  found.     In  this  book  the  page 
numbers  are  followed  by  the  paragraph  numbers,  while  the  paragraph 
symbol  (If)  and  abbreviation  (Par.)  are  replaced  by  the  colon,  thus: 
Page  29  :  4.     Furthermore,  a  distinction  is  made  between  two  classes 
of  cross  references.     Where  an  additional  statement  is  required  to  sup- 
plement the  text,  needless  repetition  may  often  be  avoided  by  reference 
to  another   paragraph.     These   references  are   important.     Other  less 
important  references  are  given  for  the  convenience  of  those  who  do  not 
grasp  the  full  significance  without  them.     Unless  a  distinction  were 
made  it  is  probable  that  students  would  either  waste  time  in  looking  up 
points  which  may  be   obvious  to   them,  or   else   they  would  become 
careless  and  fail  to  look  up  the  more  important  references.     In  order  tc 
derive  the  greatest  benefit  from  the   cross  references,   therefore,   tht 
following  interpretation  should  be  made,  viz.: 

All  references  which  appear  as  part  of  the  text  or  as  separate  sentence; 
should  be  consulted,  as  for  example:  See  page  23  :  2. 

All  references  which  appear  in  parentheses  need  be  consulted  onh 
in  case  additional  information  is  desired,  as  for  example:  (page  29  :  4) 

4.  Type.  —  Bold-faced  type  is  used  for  convenient  reference  to  shov 
the  topic  of  each  paragraph.     In  some  cases  separate  paragraph  heading; 
are  used,  but  this  plan  is  not  rigidly  adopted.     Usually  words  or  phrase; 


CHAPTER  I 


OUTLINE   OF  THE  BOOK  —  NOTATION  —  DEFINITIONS 


are.  found  which  give  the  desired  information,  and  when  these  are 
accentuated  it  seems  unnecessary  to  duplicate  them  in  special  headings. 
In  this  manner  the  more  important  parts  of  a  paragraph  are  often 
emphasized.  Fine  type  is  used  to  insert  remarks  or  explanations  at 
points  where  they  would  be  more  serviceable  than  in  footnotes,  but 
in  such  a  manner  that  the  sequence  of  the  main  text  remains  unbroken. 

1.  Formulas  are  so  often  used  blindly  by  persons  who  have  little 
conception  of  their  meaning  that  the  author  sometimes  feels  that  no 
formulas  should  be  used    by  students  lest  they  become   "  handbook 
engineers."     He  believes  that  no  one  should  use  a  formula  who  is  not 
positive  that  he  can  derive  it.     In  other  words  a  formula  should  be 
considered  an  expression  of  a  method  arranged  for  convenience  in  apply- 
ing that  method.     It  is  a  "short-cut  "  application  of  the  method  but  it 
should  not  be  used  without  a  knowledge  of  the  underlying  principles. 
Comparatively  few  formulas  are  used  in  this  book.     These   are   not 
summarized  for  reference  but  appear  only  in  conjunction  with  the  cor- 
responding derivations  which  in  turn  are  clearly  indexed.     It  is  hoped 
that  this  plan  will  tend  to  cultivate  the  proper  use  of  formulas. 

2.  Notation.  —  Considerable    annoyance    has    been    experienced    on 
account  of  the  lack  of  uniformity  in  the  notation  commonly  used  in 
formulas.     For  example,  students  constantly  confuse  bending  moments 
and  resisting  moments  in  pound-feet  with  those  in  pound-inches;   simi- 
larly in  the  usual  reduction  formulas,  they  often  substitute  the  lengths 
of  compression  members  in  feet   instead    of   in   inches.     While   these 
mistakes  are  due  chiefly  to  carelessness,  yet  they  would  be  minimized  by 
greater  uniformity.     In  this  book,  all  dimensions  in  feet,  all  moments 
in  pound-feet,  and  all  quantities  which  involve  compound  units  based 
upon  the  foot  are  expressed  by  capitals.     Similarly,  all  dimensions  in 
inches,  all  moments  in  pound-inches,  and  all  quantities  which  involve 


compound  units  based  upon  the  inch  are  (with  two  exceptions)  expressed 
by  lower-case  letters. 

The  capital  7  is  used  for  moments  of  inertia  in  inches  to  the  fourth  power,  and  the 
capital  E  is  used  for  modulus  of  elasticity  in  pounds  per  square  inch.  These  letters  are 
so  universally  and  almost  exclusively  used  that  it  seems  unwise  to  institute  a  change. 

Significant  letters,  or  letters  commonly  used,  have  been  chosen  wher- 
ever feasible,  even  though  a  single  letter  may  thus  have  more  than  one 
meaning.  It  is  felt  that  these  meanings  are  so  distinct  that  there  is 
little  chance  for  ambiguity;  further  distinction  is  made  possible  by  the 
use  of  primes  or  subscript  letters.  Letters  used  in  the  tables  at  the  end 
of  the  book  or  in  certain  other  places  are  not  included  in  the  following 
summary,  since  these  letters  have  no  special  significance  outside  of  the 
places  where  their  meanings  are  apparent.  The  term  "pound-feet" 
is  adopted  after  due  deliberation  in  preference  to  the  more  common 
term  "foot-pounds."  This  is  done  primarily  to  distinguish  the  unit  of 
moments  from  the  unit  of  work.  Both  are  compound  units  derived 
from  the  product  of  weights  or  forces  in  pounds  by  distances  in  feet; 
but  work  is  measured  by  the  product  of  a  force  by  the  distance  through 
which  the  body  acted  upon  moves,  whereas  a  moment  is  the  product  of  a 
force  by  the  perpendicular  distance  from  the  force  to  a  point  about  which 
there  is  a  tendency  to  rotate.  It  is  confusing,  for  example,  for  a  student  in 
going  from  a  class  in  Mechanics  to  one  in  Structural  Design  to  find  the 
same  term  used  for  these  two  distinct  meanings.  Furthermore,  it  seems 
more  natural  to  define  a  moment  as  "the  product  of  a  force  by  its  lever 
arm  "  rather  than  as  "  the  product  of  the  lever  arm  of  a  force  by  the  force 
itself."  In  practice  it  is  customary  first  to  select  a  force  whose  moment 
is  desired,  and  then  to  find  the  distance  from  this  force  to  the  point  of 
mpments.  Thus  it  is  logical  to  put  the  unit  of  the  force  before  the  unit 
of  the  lever  arm. 


#  =  Ib.  or  Ibs.  =  pound  or  pounds;  also  number. 
'  =  ft.  =  foot  or  feet. 
]'  =  sq.  ft.  =  square  foot  or  square  feet. 
#  ft.  =  Ib.  ft.  =  pound-feet. 
#/ft.  =  pounds  per  foot. 
jf/sq.  ft.  =  pounds  per  square  foot. 


NOTATION 


4>  =  diam.  =  diameter. 
"  =  in.  or  ins.  =  inch  or  inches. 
D"  =  sq.  in.    =.  square  inch  or  square  inches. 
#  in.  =  Ib.  ins.  =  pound-inches. 
# /in.  =  pounds  per  inch. 
#/sq.  in.  =  pounds  per  square  inch. 


PART  I  —  INTRODUCTORY 


A 
B 


n  — 


Da  = 
Dr  = 
D,  = 
Z)«,  — 


area,  in  square  feet, 
panel  length,  in  feet. 


compression. 

compressive  stress,  in  pounds  or  in  thousands  of  pounds. 


J  degree  of  curvature,  in  degrees. 

i   depth,  or  diameter,  in  feet. 

depth  from  back  to  back  of  angles,  in  feet. 

effective  depth  between  centers  of  gravity,  in  feet. 

mean  depth  between  rivet  lines,  in  feet. 

depth  between  centers  of  splice  plates,  in  feet. 

depth  of  web  plate,  in  feet. 

stress  in  rivet  at  unit  distance  from  center  of  rotation 

due  to  eccentricity,  in  pounds. 
modulus  of  elasticity,  in  pounds  per  square  inch. 


F  =  flange  stress,  in  pounds  or  in  thousands  of  pounds. 


I 


moment  of  inertia,  in  inches 4. 
conventional  sign  for  I-beam. 


a  =  area,  in  square  inches. 

back. 
b  =  \   breadth  of  beam,  in  inches. 

unit  stress  in  bearing,  in  pounds  per  square  inch. 


c  = 


center. 

width  of  strip,  in  inches. 

distance  from  neutral  axis  to  the  extreme   fiber, 
inches. 


d  =  depth,  or  diameter,  in  inches. 

db  =  depth  from  back  to  back  of  angles,  in  inches. 

da  =  effective  depth  between  centers  of  gravity,  in  inches. 

dr  =  mean  depth  between  rivet  lines,  in  inches. 

d,  =  depth  between  centers  of  splice  plates,  in  inches. 

dw  =  depth  of  web  plate,  in  inches. 


e  =  eccentricity,  in  inches. 
/  = 


rivet  stagger,  in  inches. 

unit  stress  in  the  extreme  fiber  due  to  bending,     in 
pounds  per  square  inch. 


g  =  gage,  in  inches. 

h  =  effective  depth  of  arch,  in  inches. 


fc  =  distance    in   eccentric  connections   from    the    center  of 
gravity  to  the  center  of  rotation,  in  inches. 


I  =  length,  in  inches. 


left. 

length,  in  feet. 

conventional  sign  for  angle. 

*  TV  fRr-itn's  F  and  J  f»r"  vs-d  irstead  of  lower-case  letters  in  order  to  conform  to  common  usage  (see  preceding  paragraph). 


HAPTER  I 


OUTLINE  OF  THE  BOOK  —  NOTATION  —  DEFINITIONS 


M  =  moment,  in  pound-feet. 
MB  =  bending  moment,  in  pound-feet. 
MR  =  resisting  moment,  in  pound-feet. 

P  =  concentrated  load,  in  pounds  or  in  thousands  of  pounds. 


right. 
R  =      radius  of  curvature,  in  feet. 

reaction,  in  pounds  or  in  thousands  of  pounds. 
RL  =  left-hand  reaction,  in  pounds  or  in  thousands  of  pounds. 
RR  =  right-hand  reaction,  in  pounds  or  in  thousands  of  pounds. 

S  =  stress,  in  pounds  or  in  thousands  of  pounds. 


T  = 


tension. 

tensile  stress,  in  pounds  or  in  thousands  of  pounds. 

conventional  sign  for  Tee. 


U  =  unit  load  uniformly  distributed,  in  pounds  per  foot  or  in 

thousands  of  pounds  per  foot. 
U'  =  unit  load  uniformly  distributed,  in  pounds  per  square  foot. 


V  = 


velocity,  in  feet  per  second, 
-vertical  shear,  in  pounds  or  in  thousands  of  pounds. 


W  =  total  load  uniformly  distributed,  in  pounds  or  in  thou- 
sands of  pounds. 


X 


length  of  cover  plates,  in  feet, 
unknown  distance,  in  feet. 


Y  =  unknown  distance  in  feet. 


Z  =  conventional  sign  for  Z-bar. 


m  =  moment,  in  pound-inches. 
mB  =  bending  moment,  in  pound-inches. 
•MR  =  resisting  moment,  in  pound-inches. 

f  rivet  pitch,  in  inches, 
projection  of  bearing  plate,  in  inches. 

q  =  statical  moment,  in  inches3. 


radius  of  gyration,  in  inches, 
radius  of  curvature,  in  inches. 

limiting  value  of  one  rivet,  in  pounds  or  in  thousands 
of  pounds. 

section  modulus,  in  inches3. 

•unit   stress   in  shear,  in  pounds  or   in   thousands   of 
pounds. 


t  =  thickness,  in  inches. 


v  —  intensity  of  shear,  in  pounds  per  square  inch. 


unknown  distance  in  inches. 

x  =  i  horizontal  distance  in  eccentric  connections  from  a  rivet 
to  the  center  of  gravity  of  a  group  of  rivets,  in  inches. 

y-=  vertical  distance  in  eccentric  connections  from  a  rivet  to 
the  center  of  gravity  of  a  group  of  rivets,  in  inches. 

2  =  direct  distance  in  eccentric  connections  from  a  rivet  to 
the  center  of  rotation,  in  inches. 


6 


PART  I  —  INTRODUCTORY 


+  =  sign  for  upward  forces,  for  forces  toward  the  right,  and 
for  clockwise  moments. 


-  =  sign  for  downward  forces,  for  forces  toward  the  left, 
and  for  counterclockwise  moments. 


C.  L.  or  $  =  center  line, 
b.  to  b.  =  back  to  back. 
o.  to  o.  =  out  to  out. 
D.  L.  =  dead  load. 
O.S.  =  outstanding. 


Sym.  abt.  <£  =  symmetrical  about  the  center  line. 
c.  to  c.  =  center  to  center. 

PI.  =  conventional  sign  for  plate. 
L.L.  =  live  load. 
U.M.  =  universal  mill  (for  plates  with  rolled  edges.) 

LJ  =  conventional  sign  for  channel. 

H  equation  =  (2H  =  0),  or  the  sum  of  the  horizontal  components  equals  zero. 
V  equation  =  (SF  =  0),  or  the  sum  of  the  vertical  components  equals  zero. 
M  equation  =  (SJlf  =  0),  or  the  sum  of  the  moments  equals  zero. 


DEFINITIONS 


1.  On  the  following  pages  are  summarized  brief  definitions  of  the 
engineering  terms  used  in  Parts  II  and  III  of  this  book.*  The  defini- 
tions of  some  of  these  terms  are  not  found  elsewhere,  and  the  definitions 
of  many  others  are  not  readily  accessible.  It  is  hoped  that  the  student 
will  be  encouraged  to  consult  these  pages  whenever  the  meaning  of  an 
engineering  term  is  not  fully  comprehended.  No  attempt  has  been  made 
to  give  every  interpretation  of  the  words  defined,  nor  to  define  such  com- 
mon words  as  bridge,  building,  etc.  It  is  intended  that  every  definition 
is  sufficiently  complete  to  explain  the  use  of  the  word  in  the  text. 

Abutment.   The  masonry  support  at  the  end  of  a  bridge  or  arch. 
Anchor.     A  device  for  fastening  steel  work  to  masonry. 
Anchor  Bolt.     A  bolt  which  fastens  steel  columns,  girders,  etc.,  to  masonry. 
Anchor-bolt  Plan.     A  drawing  which  shows  the  location  of  anchor  bolts. 
Angle.     A  common  structural  steel  shape  the  cross  section  of  which  is 

in  the  form  of  a  right  angle. 
Apex.     Panel  point. 

*  For  a  more  complete  glossary  of  engineering  terms,  see  Waddell's  "Bridge  Engi- 
neering," John  Wiley  and  Sons,  Inc.,  "New  York. 


Architects'  Scale.  A  measuring  scale  graduated  for  convenience  in  plot- 
ting dimensions  in  feet,  inches,  and  fractions  of  inches,  as  distinguished 
from  an  "Engineers'  Scale." 

Assembling  Marks.  A  system  of  marks  used  on  the  component  parts  of 
a  member  to  facilitate  assembling  in  the  shop. 

Axle  Load.  The  load  from  a  truck,  car,  or  locomotive  applied  to  a  struc- 
ture through  the  wheels  at  both  ends  of  the  axle,  hence  twice  the 
corresponding  "wheel  load." 

Back-check.     To  approve  or  check  the  corrections  of  a  checker. 

Base  Angle.     An  angle  which  connects  the  bottom  of  a  column  to  the 

base  plate  or  cast  base. 

Base  Plate.     A  distributing  plate  upon  which  a  column  rests. 
Batten  Plate.     A  plate  used  to  hold  the  component  parts  of  a  member 

at  the  proper  distance  apart.     Generally  used  in  conjunction  with 

lattice  bars. 
Beam.     A  member  which  resists  flexure  or  cross  bending.     Commonly 

an  I-beam  or  a  channel. 
Beam  Girder.     A  member  composed  of  two  or  more  I-beams  or  channels 

fastened  together  by  bolts  with  separators  or  by  cover  plates. 


CHAPTER  I 


OUTLINE  OF  THE  BOOK  —  NOTATION  —  DEFINITIONS 


Bearing.  The  support  upon  which  a  member  rests.  The  resistance  to 
crushing,  as  offered  by  a  member  which  bears  against  another  or 
upon  a  support,  also  as  offered  by  a  component  part  of  a  member 
to  a  rivet  or  a  pin. 

Bearing  Plate.  A  plate  used  to  distribute  the  bearing  over  a  greater 
area,  as  at  the  end  of  a  wall-bearing  beam. 

Bearing  Value.  The  amount  of  pressure  in  bearing,  either  total  or  per 
unit  of  area. 

Bed  Rock.    The  solid  rock  which  underlies  the  looser  sand,  gravel,  etc. 

Bending  Moment.  A  term  which  expresses  the  measure  of  the  tendency 
of  a  beam  to  bend.  It  is  the  sum  of  the  moments  of  all  external 
forces  on  one  side  of  the  point  of  moments. 

Bent.     A  vertical  frame  or  truss  used  to  support  other  members. 

Bevel.     The  slope  of  a  line  with  reference  to  another  line. 

Beveled  Washer.  A  cast  washer  arranged  to  compensate  for  the  inclina- 
tion between  a  bolt  or  rod  and  the  member  through  which  it  passes. 

Bill.  A  list  of  material,  such  as  a  shop  bill,  shipping  bill,  etc.  To  prepare 
such  a  bill.  Also  to  express  the  size  of  a  component  part  of  a  mem- 
ber on  the  drawing. 

Block  and  Tackle.     A  set  of  pulley  blocks  with  ropes  used  for  hoisting. 

Block  Out.     To  cut  out  by  means  of  a  rectangular  punch. 

Blueprint.  The  form  of  reproduction  of  a  drawing  which  is  issued  from 
the  drafting  department.  Blueprints  are  made  from  tracings  by 
exposing  sensitized  paper  to  the  light. 

Board  Measure.  Lumber  is  measured  in  units  of  one  foot  board  measure, 
equal  to  one-twelfth  of  a  cubic  foot,  two  dimensions  being  taken  hi 
feet  and  the  third  in  inches.  The  abbreviation  M.  B.  M.  stands  for 
"thousand  feet  board  measure." 

Bore.  To  enlarge  a  punched  hole  by  means  of  a  cutter  which  accurately 
pares  the  inner  surface. 

Box  Girder.  A  compound  girder  with  two  or  more  web  plates  which, 
with  the  cover  plates,  form  a  closed  box. 

Box  Section.  A  member  in  which  the  component  parts  enclose  a  space 
which  is  accessible  only  at  the  ends. 

Brace.  An  inclined  member  placed  between  other  members  to  make  a 
structure  more  rigid. 


Bracing  System.  A  series  of  diagonals  and  struts  placed  between  main 
members  to  resist  wind  or  other  lateral  forces. 

Bracket.  A  projecting  type  of  connection  usually  made  of  a  plate  and 
angles. 

Buckle.     To  bend  or  bow  transversely  under  the  effects  of  a  force. 

Buckle  Plate.  A  steel  plate  which  is  buckled  or  dished  at  regular  inter- 
vals to  increase  its  resistance  to  transverse  bending.  Used  in  bins 
and  in  the  floors  of  highway  bridges. 

Building  Code.  A  compilation  of  the  building  laws  and  ordinances  of 
a  city  which  relate  to  building  construction. 

Butt  Joint.  A  joint  in  which  the  ends  of  the  parts  connected  are  cut  to 
bear  against  each  other.  The  ends  are  held  in  place  by  means  of 
splice  plates,  or  similarly. 

Calk.  To  make  the  seams  of  boats,  tanks,  etc.,  watertight,  either  by 
driving  oakum  or  something  similar  into  the  seams,  or  by  forcing  the 
sharp  beveled  edge  of  one  of  two  overlapping  steel  plates  into  the 
face  of  the  other  by  means  of  an  air  hammer. 

Camber.  A  comparatively  flat  vertical  curve  placed  in  the  bottom 
chord  of  a  truss  or  girder  to  counteract  the  sag. 

Cantilever  Beam  or  Cantilever  Girder.  A  beam  or  girder  which  projects 
beyond  one  or  both  supports.  A  cantilever  beam  may  have  one  end 
embedded  in  a  wall  and  the  other  end  unsupported. 

Cap  Angle  or  Cap  Plate.  An  angle  or  plate  at  the  top  of  a  column  or 
portion  of  a  column. 

Casting.  Anything  formed  by  pouring  molten  iron,  steel,  or  other  ma- 
terial into  a  mold  and  allowing  it  to  harden. 

Center  of  Gravity.  That  point  through  which  the  resultant  of  the  par- 
allel forces  of  gravity  acting  upon  a  body  in  any  position  must 
pass.  If  the  body  could  be  supported  at  this  single  point  it  would 
remain  in  equilibrium  in  any  position. 

Center  Punch.  A  cylindrical  piece  of  steel  with  a  sharp  point  protruding 
from  one  end.  It  is  inserted  in  the  holes  of  templets  and  struck  with 
a  hammer  to  make  dents  in  the  steel  to  indicate  where  holes  are  to 
be  punched. 

Change  Order  or  Change  Slip.  An  order  issued  to  make  changes  in  the 
material  already  ordered  from  the  mills. 


8 


PART  I  —  INTRODUCTORY 


Channel.    A  common  structural  steel  shape  the  cross  section  of  which 

is  similar  to  that  of  an  I-beam  except  that  the  flanges  are  on  only 

one  side  of  the  web. 
Check.    To  approve  the  correct  portions  of  a  drawing  and  indicate  the 

mistakes.    To  verify. 
Checker.    A  person  in  the  drafting  room  who  checks  the  drawings  made 

by  others. 
Checkered  Plate.    A  steel  plate  with  raised  ribs  to  prevent  slipping. 

Used  for  floors',  stair  treads,  etc. 
Check  Marks.    Small  v-shaped  marks  or  dots  placed  over  dimensions 

or  other  quantities  to  indicate  that  they  have  been  checked. 
Chip.     To  cut  off  projecting  parts,  as  with  a  pneumatic  chisel. 
Chord.    The  main  top  or  bottom  member,  or  line  of  members,  in  a 

truss. 
Clearance.    A  space  left  between  members,  or  parts  of  members,  to  allow 

for  inaccuracies  in  cutting  and  to  facilitate  placing  them  in  position. 
Clear  Span.     The  length  of  span  from  face  to  face  of  abutments. 
Clearstory.     The  raised  portion  of  the  roof  of  a  mill  building  or  similar 

structure,  arranged  with  windows  in  the  vertical  sides. 
Clevis.     A  forging  used  to  connect  a  clevis  rod  to  a  plate  or  angle.    The 

clevis  is  arranged  to  screw  on  the  end  of  the  rod,  and  the  plate  is 

inserted  between  two  flattened  ends  through  which  a  pin  is  passed. 
Clip.    A  small  connection  angle. 
Collision  Strut.     An  auxiliary  member  which  gives  intermediate  support 

to  the  end  post  of  a  bridge. 
Column.     A  long  member,   usually  vertical,  which  resists  compression. 

It  is  the  principal  vertical  member  in  a  building. 
Column  Base.     The  cast-iron  base  or  pedestal  upon  which  a  column 

stands.     Also  the  base  plate  and  angles  riveted  to  the  bottom  of  a 

column. 
Column  Formula.     A  formula  by  means  of  which  the  allowed  unit  stress 

in  a  column  is  determined.     Its  values  depend   upon  the   ratio   of 

slenderness  of  the  column. 
Column  Schedule.    A  drawing  upon  which  is  summarized  information 

regarding  the  composition  and  the  lengths  of  different  sections  of 

the  columns  in  an  office  building. 


Combination  Sheet.    A  printed  form  upon  which  a  drawing,  a  shop  bill, 

and  a  shipping  bill  are  combined. 
Combined   Stresses.     Stresses  due  to  bending  combined  in   the  same 

member  with  direct  stresses  due  to  tension  or  compression. 
Compass.     An  instrument  for  drawing  circles. 
Component.     One  of  two  or  more  parts  into  which  a  force  or  stress  may 

be  resolved.    The  force  or  stress  is  the  resultant  of  its  components. 
Compression  Formula.    Same  as  Column  Formula. 
Compression  Member.     A  member  in  which  the  principal  stresses  tend 

to  compress  or  shorten  the  member. 
Concentrated  Load.    A  load  which  is  applied  over  such  a  small  area  or  to 

such  a  small  portion  of  a  member  or  a  structure  that  in  effect  it  may 

be  considered  as  a  single  force. 
Concrete.     An  artificial  stone  made  of  cement,  broken  stone,  sand  and 

water  which  are  first  mixed  together,  and  then  placed  in  position  and 

allowed  to  harden. 

Connection  Angle.     An  angle  used  for  connecting  other  parts.     Connec- 
tion angles  are  often  used  in  pairs. 

Connection  Plate.     A  plate  used  for  connecting  other  parts. 
Continuous  Beam  or  Continuous  Girder.    A  beam  or  girder  which  rests 

upon  more  than  two  supports. 
Contra-flexure.    A  change  in  the  direction  of  bending  in  a  column  or  a 

beam. 
Cooper's  Conventional  Loads.    A  system  of  concentrated  wheel  loads  of 

two  conventional  locomotives  followed  by  a  train,  commonly  used 

in  finding  stresses  in  railway  bridges. 

Cope.     To  cut  away  part  of  the  flange  of  a  beam  to  avoid  interference. 
Cored  Holes.     A  hole  in  a  casting  made  by  means  of  a  core  in  the  mold 

which  prevents  the  metal  from  flowing  into  the  space. 
Cornice.     The  rain-tight  junction  of  the  overhanging  roof  and  the  side 

walls  of  a  building. 
Corrugated  Steel.     Thin  sheets  of  steel  which  are  stiffened  by  having 

corrugations  rolled  in  them.    They  are  used  for  covering  the  roofs  and 

sides  of  mill  buildings. 
Cotter  Pin.    A  cylindrical  pin  held  in  place  by  a  split  steel  key  or  "cotter' 

placed  through  a  hole  in  the  pin. 


CHAPTER  I 


OUTLINE  OF  THE  BOOK  —  NOTATION  —  DEFINITIONS 


9 


Counter.  An  adjustable  diagonal  placed  across  one  of  the  panels  near 
the  center  of  a  bridge  in  the  opposite  direction  from  the  main  diagonal 
tension  member  in  the  same  panel.  Its  function  is  to  relieve  the 
main  diagonal  from  stresses  which  might  cause  compression  under 
certain  positions  of  the  live  load. 

Countersink.  To  ream  a  hole  to  receive  the  conical  head  of  a  rivet,  bolt, 
or  screw  so  that  the  end  thereof  will  not  project  beyond  the  face  of 
the  part  connected. 

Couple.  Two  equal  parallel  forces  acting  in  opposite  directions  and  in 
different  lines.  The  moment  of  a  couple  about  any  point  of  moments 
is  the  product  of  one  force  by  the  perpendicular  distance  between 
the  two. 

Cover  Angle.  A  splice  angle  placed  inside  another  angle  with  both  legs 
in  contact 

Cover  Plate.  A  plate  riveted  to  the  flanges  of  a  girder  or  compression 
member  to  increase  the  area  of  cross  section. 

Crane.  A  hoisting  machine  arranged  to  move  heavy  loads  both  verti- 
cally and  horizontally.  An  overhead  traveling  crane  is  commonly 
used  in  mill  buildings,  being  supported  by  longitudinal  girders  on 
opposite  sides  of  the  building. 

Crane  Girder  or  Crane  Runway  Girder.  A  girder  which  supports  one 
of  the  rails  upon  which  a  traveling  crane  runs.  Also  a  girder  of  the 
crane  itself. 

Crimp.  To  offset  the  end  of  an  angle  by  forging  so  it  can  overlap  another 
angle  without  the  use  of  a  filler. 

Cross  Bracing.    Bracing  with  two  intersecting  diagonals. 

Cross  Frame.     Vertical  transverse  cross  bracing  between  girders. 

Cross  Hatch.    To  draw  sloping  shade  lines  signifying  a  cross  section. 

Cross  Section.  A  transverse  section.  Also  a  view  representing  the  ap- 
pearance of  a  structure  or  member  where  cut  by  an  imaginary  sec- 
tion plane. 

Curved  Ruler.    A  guide  along  which  irregular  curved  lines  may  be  drawn. 

Dap.     To  notch  a  timber  to  fit  over  another  timber. 

Data  Sheet.  A  sheet  upon  which  are  given  the  necessary  data  for  the 
manufacturers  of  cranes,  elevators,  etc.,  that  they  may  make  them 
conform  to  the  building  requirements. 


Dead  Load.  The  comparatively  constant  static  load  on  a  structure  due 
to  its  weight,  etc.,  as  distinguished  from  the  live  or  moving  load. 

Deck  Bridge.  One  hi  which  the  principal  loads  are  applied  to  the  top 
chords. 

Deflection.  A  lateral  movement  at  right  angles'  to  the  principal  axis. 
Also  the  linear  measure  of  such  movement. 

Degree.  A  measure  of  curvature  in  railway  work.  The  degree  is  the 
angle  at  the  center  of  a  circular  curve  subtended  by  a  100-foot  chord. 

Depth.  The  principal  vertical  distance  in  a  horizontal  member  or  struc- 
ture, or  the  corresponding  dimension  in  an  inclined  member. 

Derrick.  A  hoisting  machine  so  pivoted  that  a  load  may  be  swung 
horizontally. 

Design.  To  proportion  one  or  more  members  or  parts  of  a  structure  to 
properly  fulfill  the  requirements.  Also  the  act  of  designing  or  the 
results  thereof. 

Designer.  One  who  designs.  The  title  given  to  one  whose  principal 
duty  is  to  design  structures. 

Design  Sheet.  A  drawing  prepared  by  the  designer  showing  the  prin- 
cipal dimensions  of  a  structure  and  the  sizes  of  the  designed  members. 

Detail.  To  make  a  detailed  working  drawing.  Also  a  connection  or  other 
minor  part  of  a  member  in  contradistinction  to  the  main  member. 

Detailer.  One  who  details.  The  title  given  to  a  draftsman  who  makes 
detailed  working  drawings. 

Develop.  In  drafting,  to  represent  a  bent  or  curved  part  as  if  it  were 
flattened  into  a  plane.  In  designing,  to  make  a  connection  fully  as 
strong  as  the  part  connected. 

Diagram.  An  outline  drawing  or  sketch  in  which  each  member  is  usually 
represented  by  only  a  single  line,  as  an  erection  diagram  or  stress 
diagram. 

Diaphragm.  A  stiffening  plate  or  similar  part  placed  between  the  webs 
of  a  member,  or  from  one  member  to  another. 

Die.    A  steel  form  used  in  forging  or  cutting  any  piece. 

Dimension.  A  linear  measurement  indicated  on  a  drawing  upon  a  dimen- 
sion line  which  shows  its  extent  and  significance. 

Dolly  Bar.  A  tool  for  holding  a  rivet  hi  place  while  the  opposite  end 
is  being  hammered  to  form  the  second  head. 


10 


PART   I  —  INTRODUCTORY 


Door  Post.     A  vertical  member  in  a  door  frame. 

Double  Shear.     The  tendency  to  shear,  or  the  resistance  to  shear,  in 

two  planes. 
Drafting.     Making   working  drawings,   usually  including   the   designing 

of  the  details. 
Draftsman.     One   who  drafts  or  makes  working  drawings.     The  title 

usually  includes  those  who  check  the  drawings. 

Drawing.    A  representation  by  means  of  lines  drawn  by  pencil,  pen,  etc. 
Drill.    To  make  a  hole  by  means  of  a  revolving  cutting  tool  or  drill. 
Driving  Clearance.     The  distance  from  a  rivet  to  the  nearest  projection 

which  might  interfere  with  the  use  of  the  machine  which  drives  or 

upsets  the  rivet  to  form  the  head. 
Driving  Nut.     A  nut  which  is  temporarily  screwed  on  the  end  of  a  bridge 

pin  to  protect  it  while  it  is  being  hammered  into  position. 
Eave  Strut.    A  longitudinal  strut  between  the  tops  of  the  columns  of 

a  building  at  the  eaves. 
Eccentric  Connection.     A  connection  in  which  the  line  of  action  of  the 

resultant  stress  does  not  pass  through  the  center  of  the  group  of 

connecting  rivets. 
Eccentricity.    The  distance  from  the  center  of  gravity  to  some  other 

point  or  center  line. 
Edge  Distance.    The  perpendicular  distance  from  the  center  of  a  rivet 

or  a  hole  to  the  edge  of  the  piece  which  contains  it. 
Effective  Depth.    The  depth  between  centers  of  gravity  of  the  chords, 

or  the  depth  between  the  centers  of  pins. 
Effective  Length  or  Effective  Span.    The  length  of  span  measured  from 

center  to  center  of  end  bearings. 

Elastic  Limit.     The  maximum  unit  stress  below  which  the  unit  deforma- 
tion is  proportional  to  the  unit  stress. 
Elevation.     The  vertical  distance  from  a   reference  surface  or  datum. 

Also  a  drawing  or  view  which  represents  the  projection  of  a  member 

or  structure  upon  a  vertical  plane. 
End  Frame.    The  steelwork  in  the  end  of  a  building,  especially  when 

rafters  are  used  instead  of  roof  trusses. 
End  Post.    The  vertical  or  inclined  compression  member  at  the  end  of  a 

bridge  truss. 


End  Shear.  The  shear  for  a  section  taken  near  the  end  of  a  beam  or 
girder.  In  a  simple  beam  the  section  is  taken  just  inside  of  the  result- 
ant reaction,  where  it  is  maximum. 

Engineers'  Scale  or  Decimal  Scale.  A  measuring  scale  graduated  in  inches 
and  decimals  of  an  inch,  as  distinguished  from  an  "Architects'  Scale." 

Equilibrium.  The  forces  which  act  upon  any  body  are  said  to  be  in  equi- 
librium when  they  so  balance  each  other  that  the  body  has  no  tendency 
to  move.  For  the  "equations  of  equilibrium"  see  page  183  :  2. 

Equivalent  Load.  A  load  or  system  of  loads  which  causes  the  same  effect 
as  some  other  load  or  system  of  loads. 

Erasing  Shield.  A  shield  containing  holes  of  different  shapes  through 
which  parts  of  a  drawing  may  be  erased  without  disturbing  the 
adjacent  parts. 

Erection.  The  assembling  and  the  connecting  of  the  different  members 
of  a  structure  in  their  proper  positions  at  the  site. 

Erection  Bolts.  Bolts  used  in  erection  to  hold  members  in  position  tem- 
porarily until  the  field  rivets  are  driven. 

Erection  Diagram.  An  assembly  diagram  made  to  show  the  interrela- 
tion between  the  members  of  a  structure  and  to  guide  the  erector 
in  placing  them  in  the  proper  position. 

Erection  Mark.  An  identification  mark  which  aids  the  erector  in  prop- 
erly locating  a  member.  Same  as  Shipping  Mark. 

Erection  Plan.  An  election  diagram,  more  strictly  applied  to  horizontal 
projection  rather  than  to  elevations. 

Erection  Seat.  A  seat  angle  riveted  to  a  supporting  member  to  hold  a 
girder  or  similar  member  in  position  until  the  supporting  rivets  are 
driven. 

Erector.  The  person  in  charge  of  erection,  or  collectively,  the  men  who 
erect  a  structure. 

Erector's  List.  A  list  of  the  field  rivets  and  bolts  required  to  make  the 
necessary  field  connections  in  a  structure. 

Estimate.  To  compile  the  quantities,  weights,  and  cost  of  a  structure 
usually  in  advance  of  the  construction. 

Expansion  Bolt.  A  bolt  used  for  attaching  steel  work  to  a  masonry  wall. 
The  bolt  is  surrounded  by  a  split  sleeve  which  expands  in  the  masonry 
as  the  bolt  is  tightened. 


CHAPTER  I 


OUTLINE  OF  THE  BOOK  —  NOTATION  —  DEFINITIONS 


11 


Expansion  Rollers.  A  group  of  steel  cylinders  or  segments  of  cylinders 
placed  under  the  end  of  a  bridge  girder  or  truss  to  provide  free  longi- 
tudinal movement  on  account  of  temperature  changes. 

Extension  Figure.  A  dimension  which  extends  beyond  another  dimension 
on  the  same  line,  as  for  example  to  the  end  of  a  beam  (page  86:  5). 

External  Force.  A  force  such  as  a  load  or  a  reaction  which  acts  upon  a 
member,  as  distinguished  from  an  internal  force  or  stress. 

Extreme  Fiber.     The  fiber  which  is  farthest  from  the  neutral  axis. 

Eye  Bar.  A  flat  bar  of  rectangular  cross  section  which  is  upset  at  each 
end  to  form  an  enlarged  head.  A  hole  is  bored  in  this  head  for  the 
insertion  of  a  pin. 

Fabrication.  The  shop  work  required  to  convert  the  rolled  shapes  into 
complete  structural  members,  or  in  short,  the  work  done  in  a  struc- 
tural shop. 

Face.  To  plane  or  smooth  a  surface.  Also  the  exterior  plane  surface  of 
any  solid. 

Factor  of  Safety.  The  ratio  of  the  ultimate  strength  to  the  allowed  work- 
ing' stress. 

Falsework.  A  temporary  trestle  used  to  support  a  structure  during 
erection  or  demolition. 

Fiber.  One  of  the  longitudinal  elementary  filaments  which  for  conveni- 
ence are  considered  to  exist  in  a  beam  or  similar  member. 

Field.  A  term  used  in  conjunction  with  the  work  done  on  parts  of  a  struc- 
ture at  or  near  the  site,  in  contradistinction  to  work  done  at  the  shop. 

Field  Check.  A  partial  checking  of  the  drawings  for  a  structure  to 
insure  the  proper  connection  of  the  members  in  the  field. 

Field  Connection.     A  connection  of  different  members  in  the  field. 

Field  Rivet.     A  rivet  driven  in  the  field,  as  distinguished  from  a  shop  rivet. 

Field  Splice.  A  splice  made  in  the  field,  in  distinction  to  one  made  in 
the  shop. 

Filler.     A  plate  used  to  fill  a  space  between  two  surfaces  (page  96:4). 

Fillet.  The  additional  metal  which  forms  the  curve  at  the  junction  of 
the  flange  and  the  web  of  a  rolled  shape  (page  26: 1). 

Finish.     To  smooth  a  surface  by  planing. 

Fitter.  A  shop  workman  who  assembles  the  component  parts  of  a  mem- 
ber and  bolts  them  in  position. 


Flange.  The  wider  part  of  an  I-beam  or  similar  shape  at  the  edges  of 
the  web.  Also  the  corresponding  portion  of  a  girder  or  column; 
each  flange  is  usually  composed  of  angles  or  plates  and  angles. 

Flange  Angle.     An  angle  in  a  flange  of  a  girder  or  similar  member. 

Flange  Plate.     A  plate  in  a  flange  of  a  girder  or  similar  member. 

Flange  Rivet.  A  rivet  which  attaches  the  flange  angles  to  the  web  plate 
of  a  girder. 

Flange  Splice.     A  splice  in  the  flange  of  a  girder. 

Flange  Stress.     The  stress  in  the  flange  of  a  girder  due  to  bending. 

Flat.     A  plate  not  over  7  inches  wide. 

Flexure.     Bending.    Commonly  applied  to  the  bending  of  a  beam. 

Floor  Beam.  A  beam  in  a  floor.  Also  a  transverse  beam  or  girder  placed 
at  the  panel  points  of  a  bridge  to  support  the  longitudinal  stringers. 

Floor-beam  Reaction.     The  load  upon  a  floor  beam  at  each  line  of  stringers. 

Floor  Plan.    A  plan  showing  the  arrangement  of  the  beams,  etc.,  of  a  floor. 

Floor  Plate.     A  plate  of  a  steel  floor,  such  as  used  in  a  furnace  building. 

Footing.     The  masonry  pier  or  foundation  for  a  column. 

Force.  That  which  tends  to  change  the  state  of  motion  of  a  body.  A 
force  is  known  when  its  magnitude,  direction,  line  of  action,  and 
point  of  application  are  known. 

Forging.    An  article  formed  by  being  hammered  while  hot. 

Foundation.     The  masonry  which  supports  a  steel  structure. 

Foundation  Plan.     A  plan  which  shows  the  layout  of  a  foundation. 

Function.  A  quantity  whose  value  varies  to  correspond  to  every  varia- 
tion in  some  other  quantity. 

Gable.  The  triangular  portion  of  the  end  of  a  building  between  the  oppo- 
site slopes  of  the  roof.  , 

Gage  or  Gauge.  The  distance  from  the  back  of  the  web  to  a  rivet  line 
in  the  flange  of  a  channel  or  Z-bar;  a  similar  distance  in  an  angle; 
the  distance  between  rivet  lines  in  a  angle  or  a  flange  of  another 
rolled  shape.  Also  the  clear  distance  between  the  heads  of  the  rails 
of  a  track,  standard  gage  being  4.708  ft.,  or  4'  85". 

Gas  Pipe.  Small  wrought-iron  pipe  —  often  used  in  short  lengths  for 
separators. 

Gin  Pole.  A  guyed  pole,  nearly  vertical,  equipped  with  blocks  and  tackle, 
used  for  lifting  loads. 


12 


PART  I  —  INTRODUCTORY 


Girder.  A  compound  member  usually  made  of  plates  and  angles  de- 
signed to  resist  bending  due  to  transverse  loads,  as  a  beam. 

Girt.  A  horizontal  member  in  the  side  or  end  of  a  building  used  to  sup- 
port the  side  covering  such  as  corrugated  steel. 

Government  Anchor.  A  short  rod  with  a  V-shaped  bend  in  the  center, 
used  to  anchor  the  end  of  a  wall-bearing  beam. 

Graph.  A  diagram  or  chart  used  in  determining  values  by  scaling  instead 
of  by  algebraic  computation. 

Grillage.  Tiers  of  beams  laid  across  each  other  and  imbedded  in  con- 
crete to  form  the  footing  for  a  heavily  loaded  column. 

Grip.  The  combined  thickness  of  metal  connected  by  rivets,  bolts,  or 
pins. 

Gross  Area.  The  full  area  of  cross  section,  in  contradistinction  to  net 
area. 

Grout.  A  liquid  mortar  which  can  be  poured  to  fill  small  voids  or  to 
make  a  smooth  finish. 

Guard  Rail.  Auxiliary  steel  rails  between  the  service  rails,  or  wooden 
timbers  outside  the  service  rails,  for  keeping  a  train  on  the  ties  in 
case  of  derailment. 

Gusset  Plate.  A  connection  plate  which  stiffens  a  connection,  such  as 
a  plate  which  connects  several  members  of  a  truss  or  a  bracing  system. 

Hand  Hole.  A  hole  made  for  the  insertion  of  a  hand  in  placing  bolts 
or  rivets  which  would  be  inaccessible  otherwise. 

Hanger.     A  vertical  tension  member  used  to  support  a  load. 

Heel  Plate.     A  gusset  plate  at  the  heel,  or  main  support,  of  a  roof  truss. 

Hinged  Joint  or  Hinged  Shoe.  A  joint  or  shoe  arranged  with  a  pin  or 
roller  to  permit  rotation  due  to  the  deflection  of  a  truss. 

Hip.  The  junction  of  the  top  chord  of  a  truss  with  an  inclined  end  post. 
Also  the  intersection  of  two  roofs,  provided  the  drainage  is  away 
from  the  intersection,  as  distinguished  from  a  valley. 

Hook  Bolt.     A  bolt  with  a  hook  at  the  head  end. 

I-beam.  A  common  structural  shape  the  cross  section  of  which  is  in  the 
form  of  a  letter  I. 

Impact.  The  increased  effect  of  live  loads  when  suddenly  applied.  Im- 
pact is  usually  provided  for  by  adding  a  certain  percentage  of  the 
quiescent  live  load. 


Indirect  Splice.  A  splice  in  which  the  splice  plates  or  angles  are  not  in 
direct  contact  with  the  part  spliced. 

Information  Sheet.  A  sheet  which  may  accompany  a  drawing  to  impart 
additional  information. 

Initial  Tension.  The  tension  placed  in  counters  and  in  diagonals  of 
bracing  systems  to  insure  tightness. 

Internal  Force.    A  stress  within  a  member. 

Itemize.     To  add  the  item  numbers,  etc.,  to  a  shop  bill. 

Joist.     A  beam  which  supports  wooden  flooring. 

Knee  Brace.  A  short  diagonal  brace  usually  placed  between  a  horizontal 
member  and  a  vertical  member. 

Lag  Screw.    A  large  wood  screw  with  a  square  head  like  a  bolt  head. 

Lap  Joint.     A  joint  in  which  the  connected  parts  overlap  each  other. 

Lateral.  Sidewise,  or  at  right  angles  to  the  principal  axis.  Also  a  diago- 
nal member  of  a  system  of  lateral  bracing. 

Lateral  Plate.  A  connection  plate  or  gusset  plate  hi  a  system  of  lateral 
bracing. 

Lattice  Bar.  One  of  a  series  of  zigzagged  or  crossed  bars  riveted  to 
separated  component  parts  of  a  member  to  hold  them  in  position. 

Latticed  Girder.  A  light  parallel-chord  truss  similar  to  a  plate  girder 
except  that  the  web  plate  is  replaced  by  web  members  usually  made 
of  one  or  two  angles  each. 

Laying  Out.  The  marking  of  the  steel  from  templets  or  otherwise  indicat- 
ing where  holes  are  to  be  punched  and  where  special  cuts  are  to  be 
made. 

Layout.  A  preliminary  drawing  or  sketch  by  means  of  which  distances 
may  be  determined  by  scaling. 

Lean-to.  A  building  with  a  roof  which  leans  against  another  building  or 
a  wall.  The  roof  slopes  in  one  direction  only,  the  higher  edge  being 
against  the  other  building. 

Left.  A  member  is  so  marked  when  made  exactly  opposite  a  correspond- 
ing member  marked  "right,"  the  latter  being  represented  on  the 
drawing. 

Leg.     One  of  the  two  flanges  or  parts  of  the  shape  called  an  angle. 

Lever  Arm.  The  perpendicular  distance  from  a  force  to  a  point  of  mo- 
ments. 


CHAPTER  I 


OUTLINE   OF  THE   BOOK  —  NOTATION  —  DEFINITIONS 


13 


Linear.  Pertaining  to  line  or  to  length.  A  linear  dimension  is  usually 
one  measured  parallel  to  the  length  of  a  member. 

Lintel.     A  horizontal  beam  which  supports  a  wall  over  an  opening. 

Live  Load.     A  movable  load  on  a  structure. 

Load.     The  weight  supported  by  a  structure  or  part  of  a  structure. 

Loop-rod.  A  rod  with  a  loop  at  the  end  through  which  a  pin  may  be 
passed. 

Louvres.  Series  of  horizontal  strips  of  bent  sheet  steel  arranged  along 
the  sides  of  a  monitor  to  provide  ventilation  and  at  the  same  time 
to  exclude  rain  or  snow. 

Lug.     A  small  projecting  connection,  as  a  connection  angle. 

Masonry.  A  general  term  for  structures  made  of  brick,  stone,  or  con- 
crete. 

Masonry  Plate.     A  bearing  plate  placed  on  masonry. 

Material  Order  Bill.  A  list  prepared  in  the  drafting  room  showing  the 
material  to  be  ordered  from  the  rolling  mills,  or  elsewhere. 

Member.  A  part  of  a  structure  which  is  completely  assembled  in  the 
shop  and  shipped  to  the  site  where  it  is  combined  with  other  members. 

Mill.  The  machine  or  the  plant  in  which  plates  and  shapes  are  rolled. 
Also  to  plane  the  end  of  a  member  by  means  of  a  rotary  planer  or 
milling  machine. 

Mill  Building.  A  steel-framed  building  with  a  roof  of  comparatively 
large  pitch  and  span,  but  usually  without  partitions,  intermediate 
floors,  or  intermediate  bracing. 

Milled  Joint  or  Milled  Splice.  A  joint  or  splice  in  which  the  connected 
parts  are  milled  to  bear  against  each  other. 

Milling  Machine.     See  page  31: 1. 

Mitered  Joint.  A  joint  in  which  the  angle  between  the  connected  parts 
is  bisected  by  the  plane  of  contact. 

Modulus  of  Elasticity.  The  constant  ratio  (within  the  elastic  limit)  be- 
tween the  unit  stress  and  the  unit  strain.  For  steel  of  all  grades 
this  is  between  28  and  30  million  pounds  per  square  inch. 

Moment.  The  tendency  of  a  force  to  cause  rotation  about  a  given  point. 
It  is  measured  in  compound  units  as  pound-inches  or  pound-feet 
and  is  equal  to  the  product  of  the  force  by  its  lever  arm. 

Moment  of  Inertia.    A  term  applied  to  the  sum  of  the  products  of  the 


elementary  areas  of  a  given  cross  section  by  the  squares  of  their  dis- 
tances from  a  given  axis  about  which  the  moment  of  inertia  is  said  to 
be  taken. 

Moment  Plate.-  A  splice  plate  designed  to  transmit  the  stresses  in  the 
web  of  a  plate  girder  due  to  bending  moment. 

Monitor.  The  raised  portion  of  the  roof  of  a  mill  building  or  similar 
structure,  arranged  to  give  additional  ventilation  or  light  through 
the  vertical  sides. 

Multiple  Punch.    A  machine  that  punches  two  or  more  holes  at  once. 

Nailing  Strip.  A  strip  of  wood  bolted  to  a  steel  beam  or  other  member, 
to  which  strip  wooden  flooring  or  sheathing  is  nailed. 

Net  Area  or  Net  Section.  The  effective  area  of  metal  in  a  cross  section. 
The  rectangular  areas  of  all  rivet  holes  cut  by  the  section  are  de- 
ducted from  the  gross  area  of  the  member  or  part  of  member  under 
consideration. 

Net  Width.  The  effective  width  of  metal  in  a  plate,  the  diameters  of  all 
holes  in  a  section  being  deducted  from  the  width  of  the  plate. 

Neutral  Axis.  The  intersection  of  a  cross  section  of  a  beam  or  girder 
and  the  neutral  surface. 

Neutral  Surface.  The  part  of  a  beam  which  is  neither  shortened  nor 
lengthened  when  the  beam  is  bent. 

Office  Building.  A  steel-framed  building  with  intermediate  floors  and 
columns,  and  a  comparatively  flat  roof. 

O.  G.  Washer.  A  flat  round  cast-iron  washer  commonly  used  under  a 
bolt  head  or  nut  in  timber  construction.  One  face  is  of  smaller  di- 
ameter than  the  other,  a  reverse  curve  or  "ogee"  curve  connecting 
the  two. 

Order  Bill.    A  material  order  bill. 

Orthographic  Projection.    See  page  33:  3. 

Outlooker.  A  small  angle  or  similar  piece  fastened  to  an  end  purlin  of 
a  building  to  support  the  roof  which  overhangs  the  gable  end. 

Overrun.  The  increase  in  the  actual  size  of  a  structural  shape  above  the 
size  indicated  on  the  drawing  or  order  bill. 

Oxy-acetylene  Flame  or  Torch.  An  outfit  used  for  cutting  steel  by  burn- 
ing a  narrow  slot  by  means  of  an  intense  heat. 

Packing.     The  arrangement  of  the  different  members  on  a  pin. 


14 


PART   I  —  INTRODUCTORY 


Panel.     That  part  of  a  truss  between  adjacent  panel  points. 

Panel  Point.     The  intersection  of  the  working  lines  of  different  members 

of  a  truss. 
Parabola.    A  curve  in  which  the  ordinates  vary  as  the-  squares  of  the 

abscissas,  or  conversely.     For  the.  construct  on,  see  page  260. 
Pattern.     A  wooden  model  for  a  casting,  used  in  forming  the  mold. 
Pedestal.     A  cast-steel  or  cast-iron  stool  or  support  for  a  bridge  girder. 
Piece  Mark.     An  assembling  mark. 
Pier.     An  intermediate  masonry  support  for  a  bridge.     Also  a  column 

footing. 
Pilot  Nut.     A  nut  which  is  temporarily  screwed  on  the  end  of  a  bridge 

pin  to  guide  it  while  it  is  being  driven  into  position. 
Pin.    A  steel  cylinder  used  for  connecting  the  members  of  a  truss,  or 

similarly. 
Pin  Plate.     A  reinforcing  plate  riveted  to  a  truss  member  to  give  greater 

bearing  on  a  pin. 
Pitch.     The  longitudinal  distance  between  adjacent  rivets  in  the  main 

part  of  a  member.    Also  the  ratio  of  the  center  height  of  a  roof  truss 
'  to  the  span. 
Plan.     A  drawing  which  represents  the  horizontal  projection  of  a  struc- 

.     ture  or  part  of  a  structure. 
Plane.    To  smooth  to  a  plane  surface. 

Plate.     A  flat  piece  of  rolled  steel  of  rectangular  cross  section. 
Plate  Girder.    A  built  beam  with  a  solid  web  plate  to  which  are  riveted 

two  flanges  composed  of  angles  or  angles  and  plates. 
Pneumatic  Chisel.     A  cutting  tool,  operated  by  compressed  air,  used 

for  cutting  off  projecting  parts. 
Pneumatic  Reamer.    A  reaming  tool,  operated  by  compressed  air  used 

for  enlarging  holes. 
Point  of  Moments.     A  point  where  moments  are  taken,  i.e.,  from  which 

the  lever  arms  of  the  forces  are  measured. 
Pony  Truss.     A  bridge  truss  which  is  not  deep  enough  to  permit  the  use 

of  overhead  bracing  between  the  trusses. 
Portal   Bracing.     The   bracing   in   the   plane  of   the   end   posts   of   a 

bridge. 
Post.     A  comparatively  small  compression  member,  usually  vertical. 


Projection  Line.    A  line  drawn  at  right  angles  to  a  dimension  line  to  indi- 
cate the  extent  of  the  dimension. 
Punch.     To  make  a  hole  as  explained  on  page  29  : 5.     Also  a  punching 

machine. 
Purlin.     A  horizontal  longitudinal   member  which  rests   upon  the  top 

chords  of  roof  trusses  to  support  the  roof. 
Radius  of  Gyration.     The  distance  from  an  axis  of  rotation  to  the  center 

of  gyration.    Numerically  it  is  equal  to  the  square  root  of  the  quo- 
tient of  the  moment  of  inertia  about  the  same  axis  divided  by  the 

corresponding  area. 
Rafter.    An  inclined  member  parallel  to  the  roof  slope  which  is  used 

either  to  support  the  purlins  in  place  of  a  truss,  or,  resting  upon  the 

purlins,  to  support  the  roofing. 
Rail  Clamp.     A  small  casting  used  for  fastening  a  crane  rail  to  the  flange 

of  a  supporting  girder. 
Ratio  of  Slenderness.    The  ratio  of  the  length  of  a  compression  member 

to  the  least  radius  of  gyration  of  its  cross  section. 
Reaction.     The  force  on  a  beam,  girder,  or  truss  imparted  by  the  support. 

It  is  equal  and  opposite  to  the  pressure  of  the  beam  on  the  support. 
Ream.     To  enlarge  a  hole  by  means  of  a  rotating  fluted  cutter. 
Reduction  Formula.    Same  as  column  formula. 
Reinforced   Concrete.       Concrete   in    which   steel   bars   are   placed   to 

strengthen   it. 
Reinforcing  Plate.    A  plate  used  to  strengthen  the  weaker  part  of  a 

member  to  develop  the  strength  of  the  remaining  parts. 
Resisting  Moment.     The  moment  of  the  internal  forces  which  resist  the 

bending  moment  on  a  beam  or  girder. 

Restrained  Beam.     A  beam  which  is  restrained  or  "fixed"  at  a  support. 
Resultant  or  Resultant  Force.     The  simplest  single  force  or  system  of 

forces  which  can  replace  a  system  of  forces  and  have  an  equivalent 

effect. 
Reversal  of  Stress.    The  changing  of  stress  from  tension  to  compression, 

or  vice  versa. 

Ridge  Strut.     A  longitudinal  strut  along  the  ridge  or  peak  of  a  roof. 
Right.     A  member  is  so  marked  when  another  member  marked  "left" 

is  to  be  made  exactly  opposite  from  the  same  drawing. 


CHAPTER  I 


OUTLINE  OF  THE  BOOK  —  NOTATION  —  DEFINITIONS 


15 


Right  Section.     A  section  at  right  angles  to  the  principal  axis. 

Rivet.  A  short  cylindrical  rod  of  steel  with  upset  heads  used  to  rivet 
or  fasten  together  component  parts  of  a  steel  structure.  One  head  is 
formed  before  the  rivet  is  put  in  position,  the  other  afterward. 

Rivet  Code.  The  conventional  representation  of  rivets  under  different 
conditions. 

Riveter.  One  who  rivets  or  operates  a  riveting  machine.  A  riveting  ma- 
chine. Also  an  instrument  for  drawing  small  circles  to  represent  rivets. 

Rivet  Line.     A  line  through  the  centers  of  a  series  of  rivets. 

Rivet  Pitch.  The  longitudinal  distance  between  adjacent  rivets  in  the 
main  part  of  a  member. 

Rivet  Spacing.     The  dimensions  which  locate  the  centers  of  rivets. 

Rocker.  A  hinged  shoe  with  a  pin  or  other  device  to  prevent  unequal 
distribution  of  pressure  upon  the  masonry  when  the  supported 
girder  or  truss  deflects. 

Rod.     A  rolled  bar  of  steel  with  round  or  square  cross  section. 

Roller.  A  steel  cylinder  or  segment  of  a  cylinder  placed  under  one  end 
of  a  bridge  girder  or  truss  to  facilitate  longitudinal  movement  on 
account  of  temperature  changes.  Groups  of  rollers  are  held  in  place 
by  a  roller  box,  the  whole  forming  a  roller  nest. 

Rolling  Mill.  The  machine  or  the  plant  in  which  plates  and  shapes  are 
rolled. 

Rotary  Planer.    See  page  31  : 1. 

Rough  Bolt.  An  ordinary  bolt,  as  distinguished  from  a  turned  bolt  or 
machine  bolt. 

Round.    A  round  rod. 

Ruling  Pen.     An  instrument  for  drawing  ink  lines. 

Safe  Load.  A  load  which  can  be  supported  by  a  member  without  over- 
stressing  the  member.  More  commonly  the  maximum  safe  load. 

Sag  Rod.  A  vertical  or  inclined  tie  rod  used  to  prevent  a  girt  or  a  purlin 
from  sagging. 

Saw-tooth  Roof.    See  page  113  :  2. 

Scale.  A  flat  or  triangular  measuring  stick  used  in  plotting  a  drawing 
in  proportion  to  the  thing  represented  Also  this  proportion. 

Seat  Angle.  A  small  angle  riveted  to  one  member  to  support  the  end  of 
a  beam  or  girder. 


Secondary  Stress.  An  indirect  stress  which  results  because  the  ideal 
conditions  upon  which  the  calculation  of  the  principal  or  primary 
stresses  is  based  are  not  realized. 

Section.  A  cut  across  a  member  or  structure  made  by  an  imaginary 
plane.  Also  used  in  place  of  "sectional  view." 

Sectional  View.  The  projection  of  one  segment  of  a  member  or  structure 
upon  a  section  plane. 

Section  Line.  To  shade  a  sectional  view  by  means  of  fine  sloping  lines 
representing  the  parts  cut  by  a  section  plane. 

Section  Modulus.  The  quotient  of  the  moment  of  inertia  of  a  cross  sec- 
tion of  a  member  by  the  distance  from  the  neutral  axis  to  the  extreme 
fiber. 

Section  Plane.     An  imaginary  plane  which  cuts  a  section. 

Selvage  Edge.  The  original  woven  edge  of  a  piece  of  cloth  where  the 
threads  are  closer  together  than  in  the  body  of  the  cloth. 

Separator.  A  casting  or  piece  of  gas  pipe  placed  between  the  webs  of 
beams  to  keep  them  a  fixed  distance  apart. 

Shank.  The  cylindrical  part  of  a  rivet  or  bolt,  as  distinguished  from  the 
head. 

Shape.  A  general  term  for  rolled  steel  of  any  cross  section  other  than  a 
plate. 

Shear.  To  cut  by  shearing  (page  28: 1).  Also  an  expression  for  the 
algebraic  sum  of  certain  forces  which  tend  to  shear  a  member. 

Sheared  Plate.  A  plate  which  is  rolled  between  two  rolls  and  then 
sheared  to  the  desired  width  at  the  mill,  as  distinguished  from  a 
Universal  Mill  plate  which  is  rolled  to  the  desired  width  by  means 
of  supplementary  rolls. 

Shearing  Stress.     The  internal  forces  which  resist  the  tendency  to  shear. 

Shearing  Value.    The  strength  of  a  rivet,  pin,  or  bolt  in  resisting  shear. 

Shear  Intensity.    The  shearing  stress  per  unit  area. 

Shears.     A  machine  for  shearing. 

Sheathing.     A  wooden  covering  of  planks  or  boards. 

Shipping  Bill.  A  list  of  members  to  be  shipped  from  the  shop  to  the 
site. 

Snipping  Mark.  An  identification  mark  assigned  to  each  separate  mem- 
ber shipped. 


16 


PART   I  - INTRODUCTORY 


Shoe.    The  part  of  a  bridge  that  transmits  the  load  from  the  end  pin  of 

a  truss  to  the  bearing  plate  or  rollers. 
Shop.     The  place  where  the  component  parts  of  a  structure  are  fabricated 

into  members. 
Shop  Bill.     A  summary  of  material  required  for  fabricating  members  in 

the  shop. 

Shop  Drawing.     A  working  drawing  prepared  for  use  in  the  shop. 
Shop  Rivet.     A  rivet  which  is  driven  in  the  shop,  as  distinguished  from 

a  field  rivet  driven  at  the  site. 

Sidewalk  Bracket.     A  bracket  which  supports  the  sidewalk  of  a  bridge. 
Simple  Beam.    An  unrestrained  beam  which  is  supported  at  both  ends 

only. 

Single  Punch.    To  punch  one  hole  at  a  time. 
Single  Shear.    The  tendency  to  shear,  or  the  resistance  to  shear,  in  one 

plane. 

Site.    The  final  location  of  a  structure. 
Sketch  Plate.     An  irregular  plate  which  is  cut  to  dimension  at  the  mill 

according  to  a  sketch. 
Sketch  Sheet.    A  small  sheet  or  printed  form  upon  which  a  drawing  is 

made. 
Skewback.    An  auxiliary  angle  or  other  support  for  a  floor  arch.    Also 

a  bent  plate  or  casting  used  to  attach  a  diagonal  rod. 
Skew  Bridge  or  Skew  Span.    A  bridge  or  span  which  does  not  cross  a 

stream  or  roadway  at  right  angles;   the  end  of  one  truss  or  girder  is 

not  opposite  the  end  of  the  other  truss  or  girder. 
Skew  Portal.     The  portal  or  the  portal  bracing  of  a  skew  bridge. 
Skids.     Parallel  supports  of  timber  or  metal  used  to  elevate  members  a 

convenient  distance  above  the  floor  of  the  shop  to  make  them  more 

accessible. 
Slab.    A  flat  solid  of  considerable  area  but  of  relatively  small  thickness, 

such   as    a   portion   of    a    concrete    floor   between   the   supporting 

beams. 
Sleeve  Nut.    A  long  tubular  nut  having  a  right-handed  thread  in  one 

half  and  a  left-handed  thread  in  the  other,  used  for  joining  two  rods 

and  pulling  them  together  to  tighten  them. 
Slope.    The  bevel  or  inclination  of  one  line  with  reference  to  another; 


it  is  measured  by  the  tangent  of  the  angle  of  inclination  expressed 

in  inches  to  a  base  of  one  foot. 
Slotted  Hole.     An  elongated  hole  with  semi-circular  ends  and  parallel 

sides. 
Sole  Plate.     A  plate  riveted  to  the  bottom  of  a  plate  girder  to  bear  upon 

a  masonry  plate. 
Solid  Floor.     Any  type  of  floor  construction  other  than  the  so-called 

open  floor  of  a  railway  bridge  in  which  the  ties  rest  directly  upon  the 

stringers  or  girders. 
Span.     The  distance  between  the  supports  of  a  beam,  girder,  truss,  etc- 

Also  a  bridge  or  similar  structure  which  spans  an  opening. 
Specifications.     That  part  of  a  contract  which  prescribes  the  allowed 

unit  stresses  and  gives  directions  and  restrictions  regarding  proper 

construction. 

Spiking  Piece.     A  wooden  strip  bolted  to  a  steel  beam  or  similar  mem- 
ber to  which  strip  planking  or  sheathing  may  be  spiked. 
Splice.     The  connection  of  two  similar  members  or  segments  of  mem- 
bers in  the  same  straight  line. 

Splice  Angle  or  Splice  Plate.     An  angle  or  plate  used  in  a  splice. 
Staggered  Rivets.     Rivets  which  alternate  on  two  parallel  rivet  lines. 
Statical  Moment.     The  product  of  an  area  by  the  distance  from  an  axis 

to  the  center  of  gravity  of  the  area  (see  page  202  : 1). 
Statics.     That  branch  of  Mechanics  which  has  to  do  with  systems  of 

balanced  forces  acting  upon  bodies  at  rest. 

Steel.     A  modified  form  of  iron  used  in  construction.     See  Chapter  III. 
Stiffener  or  Stiffening  Angle.     An  angle  used  to  prevent  a  plate  from 

buckling  or  to  prevent  a  seat  angle  from  bending. 
Stitch  Rivets.     Rivets  placed  at  comparatively  long  intervals,  usually 

in  a  member  composed  of  two  angles,  to  hold  the  component  parts 

together  and  to  equalize  the  stress  between  them. 
Straight-edge.    A  thin  strip  of  wood,  metal,  or  celluloid  with  a  straight 

edge  used  as  a  guide  in  drawing  straight  lines. 
Strain.     The  deformation  in  a  member  caused  by  an  external  force.    Strain 

is  measured  in  linear  units. 
Stress.     An  internal  force  which  resists  the  tendency  of  an  external  force 

to  change  the  shape  of  the  body. 


CHAPTER  I 


OUTLINE  OF  THE   BOOK  —  NOTATION  —  DEFINITIONS 


17 


Stress  Diagram.  A  diagram  by  means  of  which  stresses  are  determined 
graphically.  Also  a  stress  sheet. 

Stress  Sheet.  A  sheet  upon  which  is  recorded  the  stresses  in  the  prin- 
cipal members  of  a  structure. 

Stringers.  The  longitudinal  members  which  support  the  track  or  the 
floor  of  a  bridge.  They  are  supported  by  transverse  floor  beams. 

Structural  Company.  A  company  engaged  in  the  construction  of  steel 
structures. 

Structural  Drafting.  The  preparation  of  the  working  drawings  for  the 
members  of  a  steel  structure,  such  as  a  bridge,  a  building,  a  tower, 
etc. 

Structural  Shop.  A  shop  where  the  rolled  steel  shapes  are  punched,  cut, 
riveted,  and  otherwise  prepared  for  use  in  a  steel  structure. 

Strut.  A  comparatively  light  compression  member,  usually  with  no 
intermediate  connection. 

Sub-punch.    To  punch  to  a  smaller  diameter. 

Substructure.  The  masonry  abutments,  piers,  or  foundation  for  a  steel 
structure. 

Super-elevation.  The  vertical  distance  between  the  tops  of  the  rails  of  a 
track  on  a  curve. 

Superstructure.  The  main  part  of  a  structure  above  the  masonry  founda- 
tion or  "substructure." 

Sway  Bracing.  Bracing  in  a  vertical  plane,  as  between  the  columns  of 
a  building  or  between  the  trusses  of  a  bridge. 

Swedge  Bolt.  An  anchor  bolt  with  a  nut  at  one  end  but  with  elliptical 
depressions  near  the  other  end  to  furnish  greater  bond  when  im- 
bedded in  masonry. 

Tamp.     To  compact  concrete,  dirt,  or  other  material  by  pounding. 

Tee  or  T-iron.  A  structural  shape,  the  cross  section  of  which  is  in  the 
form  of  a  letter  T. 

Templet.  A  strip  of  wood  upon  which  holes,  cuts,  etc.,  are  laid  out  and 
from  which  the  steel  is  marked  accordingly. 

Templet  Maker.     One  who  makes  templets. 

Templet  Shop.     The  shop  where  templets  are  made. 

Tension  Member.  A  member  in  which  the  principal  stresses  tend  to 
lengthen  the  member. 


Through  Bridge.  One  hi  which  the  principal  loads  are  applied  to  a  floor 
system  near  the  bottom,  and  the  trams,  etc.,  pass  "through"  the 
structure  between  the  trusses  or  girders. 

Tie.  A  light  tension  member,  such  as  the  diagonal  in  a  bracing 
system.  Also  a  transverse  timber  which  supports  the  rails  of  a 
track. 

Tie  Plate.  A  plate  used  to  hold  the  component  parts  of  a  member  at  the 
proper  distance  apart.  Generally  used  hi  tension  members  or  else  in 
conjunction  with  lattice  bars. 

Tier.    A  row  or  layer  placed  above  or  below  a  similar  row  or  layer. 

Tie  Rod.  A  short  rod  used  to  tie  the  beams  of  a  floor  together  in  order 
to  counteract  the  thrust  from  floor  arches.  Also  a  rod  used  similarly 
elsewhere. 

Trace.  To  copy  a  drawing  or  portion  of  a  drawing  upon  a  superimposed 
transparent  sheet  of  tracing  cloth  or  paper. 

Tracer.  One  who  traces.  A  title  given  to  a  person  in  a  drafting  room 
whose  chief  duty  is  to  trace  drawings  made  by  others. 

Tracing.     A  drawing  on  tracing  cloth. 

Tracing  Cloth.  A  linen  cloth  specially  treated  to  make  it  transparent 
for  use  in  copying  drawings  by  tracing  and  blueprinting. 

Track.  The  rails,  including  their  supports,  along  which  a  body  or  struc- 
ture with  wheels  or  rollers  may  be  rolled.  The  track  on  a  railway 
bridge  includes  not  only  the  service  rails  and  the  ties,  but  also  the 
guard  rails,  and  the  bolts,  spikes,  and  other  fastenings. 

Traveler.  A  form  of  derrick  used  in  erection;  it  is  mounted  on  wheels 
so  that  it  may  be  advanced  as  the  work  progresses. 

Triangle.  A  flat  piece  of  celluloid  or  similar  material  used  in  drafting. 
The  three  edges  form  a  right  tr'angle,  and  the  complementary  angles 
are  usually  45°,  or  else  30°  and  60°. 

Truss.  A  framed  structure  which  acts  as  a  beam  The  principal  mem- 
bers form  a  series  of  triangles,  and  each  member  is  primarily  sub- 
jected to  axial  stress  only. 

T-square.  A  T-shaped  drawing  instrument  with  a  long  thin  blade  at- 
tached to  a  shorter  thicker  head.  The  blade  is  used  as  a  straight- 
edge for  drawing  parallel  lines  as  the  head  is  moved  along  the  end 
of  the  drawing  board. 


18 


PART  I  -  INTRODUCTORY 


Turnbuckle.  Similar  to  a  sleeve  nut  except  that  a  transverse  opening  is 
provided  at  the  center  for  the  insertion  of  a  crow-bar  by  means  of 
which  the  turnbuckle  may  be  turned.  See  sleeve  nut. 

Turned  Bolt.    A  machine  bolt  which  is  cut  in  a  lathe  to  accurately  fit  a  hole. 

U-bolt.     A  rod  bent  in  the  shape  of  the  letter  U  with  nuts  on  each  end. 

Underrun.  The  decrease  in  the  actual  size  of  a  structural  shape  below 
the  size  indicated  on  the  drawing  or  order  bill. 

Uniform  Load  or  Uniformly  Distributed  Load.  A  load  which  is  uni- 
formly distributed  over  a  given  distance. 

Unit  Stress.     The  stress  per  unit  of  area,  or  the  intensity  of  stress. 

Universal  Mill  Plate  or  U.  M.  Plate.  A  plate  rolled  in  a  Universal  Mill 
which  is  provided  with  vertical  rolls  as  well  as  horizontal  rolls.  A 
plate  with  rolled  edges,  as  distinguished  from  a  sheared  plate. 

Upset.  To  enlarge  the  end  of  a  rivet,  a  rod,  an  eye  bar,  etc.,  by  hammer- 
ing or  pressing  into  a  die  while  hot. 

Valley.  The  intersection  of  two  roofs  provided  the  drainage  is  toward 
the  intersection,  as  distinguished  from  a  hip. 

Vertical  Flange  Plate.  A  vertical  plate  in  the  flange  of  a  plate  girder, 
either  between  the  web  and  a  flange  angle  or  outside  the  vertical  leg 
of  an  angle. 

View.  In  orthographic  projection,  a  view  is  the  projection  of  an  object 
upon  a  plane  by  means  of  parallel  lines. 


Washer.     Usually  a  flat  disc  with  a  central  hole,  used  under  the  head 

or  the  nut  of  a  bolt,  or  similarly. 
Web.     The  web  plate  of  a  girder,  column,  or  other  built  member,  or  the 

corresponding  thin  portion  between  the  flanges  of  an  I-beam,  channel, 

etc. 
Web  Member.     An  intermediate  member  of  a  truss  or  latticed  girder 

between  the  chords. 
Web  Plate.     The  main  plate  of  a  plate  girder,  column  or  similar  member, 

connecting  the  two  flanges. 
Web  Splice.     A  splice  in  a  web  plate. 
Wheel  Load.     The  load  from  a  truck,  car,  or  locomotive  applied  to  a 

structure  through  a  wheel. 
Wind  Bracing.     A  system  of  bracing  which  resists  stresses  induced  by 

the  wind. 

Wind  Load.     A  load  on  a  structure  due  to  wind  pressure. 
Working  Line.     A  reference  line  to  which  the  dimensions  of  a  member  are 

referred;  usually  used  in  conjunction  with  the  working  lines  of  other 

members  to  form  a  system  of  working  lines  of  a  truss,  latticed  girder, 

of  bracing  system. 

Working  Point.     The  intersection  of  two  or  more  working  lines. 
Z-bar.     A  structural  shape  the  cross  section  of  which  is  in  the  form  of 

the  letter  Z. 


CHAPTER  II 


THE   ORGANIZATION   OF  A   STRUCTURAL   COMPANY  — THE 
ENGINEERING   DEPARTMENT 

SYNOPSIS:  The  student  should  have  a  conception  of  the  relation  which  the  structural 
steel  drafting  department  bears  to  other  branches  of  the  steel  industry.  An  abstract 
is  giveVi  in  Chapters  II,  III,  and  IV. 


1.  The  structural  draftsman  is  not  concerned  directly  with  the  manu- 
facture of  steel  or  even  with  the  rolling  of  the  commercial  steel  "shapes." 
His  drawings  show  how  these  shapes  are  cut,  punched,  and  assembled 
to  form  members  which  in  turn  go  to  make  steel  structures.     But  every 
draftsman  should  understand  the  processes  which  are  allied  to  the  work 
of  his  company.     The  student  has  no  time  for  a  careful  study  of  the 
different  operations,  but  he  should  have  a  general  idea  of  how  steel  is 
made  and  used.     For  his  convenience  an  abstract  is  presented  in  this 
chapter  and  in  the  two  subsequent  chapters.     Later  he  may  acquire 
further  knowledge  from  books  or  from  inspection  trips  to  rolling  mills, 
to  structural  shops,  and  to  erection  sites. 

2.  In  the  Estimating  or  Designing  Department  of  a  structural  com- 
pany are  made  the  preliminary  design  and  the  estimate  of  cost  of  a 
proposed  structure.     These  may  be  based  upon  the  customer's  layout, 
or  upon  an  original  design  submitted  to  the  customer  for  approval. 
Usually  several  different  companies  furnish  estimates  in  competition. 
After  a  contract  is  awarded  the  design  sheet  is  forwarded  to  the  Detail- 
ing or  Drafting  Department.     The  design  sheet  usually  shows  the  main 
form  and  dimensions  of  the  structure,  the  principal  stresses,  and  the 
sizes  of  all  main  members,  together  with  special  instructions  regarding 
the  details.     The  work  of  the  Designing  Department  is  explained  more 
fully  on  page  20:  2. 

3.  In  the  Drafting  Department  the  detailed  working  drawings  are 
prepared  for  use  in  the  shop.     Various  diagrams  and  lists  are  also  made, 


19 


such  as  the  preliminary  bills  of  material  from  which  the  steel  shapes  are 
ordered  from  the  rolling  mills.  As  far  as  possible,  the  material  must  be 
ordered  before  the  drawings  are  made  so  that  the  mills  may  roll  the 
steel  while  the  drawings  and  the  templets  are  being  prepared.  As  soon 
as  the  drawings  are  made  and  checked,  blueprints  are  sent  to  the 
templet  shop,  to  the  structural  shop,  and  to  others  concerned. 
The  work  of  the  Drafting  Department  is  described  more  fully  on 
page  20:  4. 

4.  The  drawings  are  first  sent  to  the  templet  shop  where  templets 
are  made  for  most  of  the  members.     These  templets  are  virtually  pat- 
terns for  cutting  and  punching  the  component  pieces.     They  are  usually 
made  of  wood.     Not  only  can  the  work  be  laid  out  on  wood  with  greater 
facility  than  on  steel  but  the  templets  can  often  be  completed  before  the 
steel  arrives  from  the  rolling  mills  and  thus  the  completion  of  the  struc- 
ture is  hastened.     Furthermore,  the  work  may  be  laid  out  on  wood 
once  and  then  the  templets  may  be  used  repeatedly  in  marking  many 
steel  pieces  which  are  alike  or  similar. 

5.  The  manufacture  of  steel  and  the  rolling  of  the  structural  shapes 
are  described  in  the  next  chapter.     The  finished  shapes  are  shipped  to 
the  structural  shop  where  all  cuts  and  holes  are  first  indicated  on  the 
steel  by  means  of  the  templets.     The  steel  is  then  taken  to  shears  to 
be  cut  and  to  punches  to  have  the  rivet  holes  punched.     The  com- 
ponent parts  of  each  member  are  then  assembled,  being  held  together 
temporarily  by  bolts  until  the  shop  rivets  are  driven.     Other  proc- 


20 


PART  I  —  INTRODUCTORY 


esses  may  be  required  on  some  members  before  thay  are  painted  and 
shipped,  as  described  more  fully  in  Chapter  IV,  page  27. 

1.  Erection.*  —  The  different  members  of  a  structure  are  shipped  to 
the  site  as  far  as  practicable  in  the  proper  sequence  for  erection.     The 
methods  of  erecting  them  differ  with  the  size  and  the  type  of  the  struc- 
ture and  with  its  location.     Usually  buildings  are  made  self-supporting 
from  the  first,  but  truss  bridges  must  be  supported  by  "false  work  " 
or  by  other  means  until  they  are  nearly  complete.     Locomotive  cranes 
are  used  extensively  in  the  erection  of  mill  buildings,  girder  bridges,  and 
viaducts.     Derricks  are  used  for  office  buildings  and  "travelers"  for 
truss  bridges.     Main  members  are  usually  placed  in  position  first  and 
secondary  members  are  filled  in  afterwards.     Enough  erection  bolts 
are  used  to  hold  the  members  in  position  until  the  "riveting  gangs" 
can  drive  permanent  rivets. 

THE  ENGINEERING  DEPARTMENT  f 

2.  The  Engineering  Department  includes  the  Designing  or  Estimat- 
ing  Department  and   the   Drafting  or  Detailing   Department.     Both 
departments  are  in  charge  of  a  Chief  Engineer  and  often  one  or  more 
Assistant   Chief   Engineers,   although  these   officers   are   usually  more 
directly  concerned  with  the  work  of  the  Designing  Department.     The 
organization  of  the  Designing  Department  differs  in  different  companies 
and  the  procedure  depends  upon  the  organization  and  also  upon  the 
nature  and  the  magnitude  of  the  proposed  structures.     Some    com- 
panies have  a  special  contracting  Department  which  acts  as  interme- 
diary between  the  Designing  Department  and  the  customers.     Some 
designs  are  made  by  the  customer's  engineers  or  by  consulting  engineers, 
and  the  structural  companies  simply  estimate  the  cost  and  submit  bids. 
Some  structures  are  so  simple  or  so  similar  to  other  structures  that  the 
designers,  or  the  contracting  engineers  in  charge  of  branch  offices,  can 
make  quite  accurate  estimates  quickly  without  complete  designs.     Of  ten- 

*  See  Thayer's  "Structural  Design,"  Vol.  I,  D.  Van  Nostrand  Co.,  New  York,  and 
Merriman  and  Jacoby's  "Roofs  and  Bridges,"  Vol.  Ill,  John  Wiley  and  Sons,  Inc., 
New  York.  For  erection  tools  and  specifications  see  Ketchum's  "Structural  En- 
gineers' Handbook,"  McGraw-Hill  Book  Co.  Inc.,  New  York. 

t  See  also  Tyrrell's  "Mill  Buildings,"  The  McGraw-Hill  Book  Co.  Inc.,  New  York. 


times  the  customer  has  little  conception  of  the  type  of  structure  best 
suited  to  his  needs  and  the  structural  companies  prepare  alternate 
designs  from  which  the  customer  may  make  selection. 

3.  Design  sheets  or  stress  sheets  are  made  by  the  designer  or  by  a 
draftsman   under   his   direction   to   illustrate   the   proposed    structure. 
They  show  the  general  form  of  the  structure,  the  principal  dimensions 
and  stresses,  and  the  composition  of  each  main  member,  as  illustrated 
in  Fig.  21.     The  design  is  made  according  to  specifications  approved 
by  the  customer.     An  estimator  must  have  an  intimate  knowledge  of 
drafting  room   methods   and   of  shop   methods  and   costs.     He   must 
know  from  experience  how  much  to  allow  for  the  details  of  construction 
such  as  connection  plates  and  angles.     He  must  be  familiar  with  the 
methods  of  erection  and  be  able  to  determine  the  method  best  adapted 
to  a  given  structure  in  a  given  location.     The  estimator  may  be  assisted 
by  draftsmen,  tracers,  and  computers.     As  soon  as  a  contract  is  awarded, 
the  design  sheet  is  adapted  to  the  needs  of  the  Drafting  Department 
and  any  necessary  alterations  or  additions  are  made.     The  design  sheet 
should  give  all  information  necessary  to  enable  the  draftsmen  to  make 
the  detailed  drawings.     It  may  be  supplemented  by  an    "information 
sheet "  which  gives  the  principal  terms   of  the   contract  such  as  the 
time  of  delivery  and  whether  the  cost  is  quoted  at  a  "lump  sum  "  or 
at  a  price  per  pound. 

4.  The  Drafting  Department  is  in  charge  of  a  Chief  Draftsman. 
His  subordinate  draftsmen  are  usually  divided  into  squads,  each  in 
charge  of  a  "squad  foreman  "  or  "squad  boss."     The  drawings  for  each 
contract  are  usually  all  made  in  one  squad,  the  drawings  for  other  con- 
tracts often  being  carried  on  simultaneously.     The  size  of  each  squad 
varies  with  the  amount  of  work  being  done  under  the  direction  of  a 
single  squad  foreman  from  3  or  4  to  16  or  20,  the  normal  number  being 
from  6  to  8.     In  each  squad  are  checkers,  detailers,  tracers,  billers,  and 
computers.     The  detailers  make  the  working  drawings,  and  design  the 
details.     The  drawings  show  how  the  standard  shapes  are  cut  and  com- 
bined to  form  the  different  members.     The  number  and  the  spacing  of 
the  rivets  are  given  so  that  the  members  may  be  properly  constructed 
and  so  that  they  may  be  easily  connected  to  other  members  in  the 
structure.     As  far  as  practical  the  parts  are  combined  in  the  shop  in 


CHAPTER  II 


THE  ORGANIZATION   OF  A  STRUCTURAL  COMPANY 


21 


68-0     c.  to  c.  bearings 


70-0"t>.  to  b.  La 


Stringer 


HALF  END  VIEW 


Base  of  Raft 


HALF  SECTION 


/ 
\ 


SPECIFICATIONS  -  AMER,  BY,   £TVG.   ASS'N.  -  1910 

MATERIAL  -  STRUCTURAL  0.  H.  STEEL 

RIVETS-  j" 

TIES  -  8x  9  x  IO-0"NOTCHED  TO  8f 

ASSUMED  DEAD  LOAD  OF  TRACK  -  400*/FT. 

ASSUMED  LIVE  LOAD  -  COOPER'S    E  BO 


GIRDERS 

MOMENT 
D=  6,980,000 
LK2S,  810,000 
1=23,420,000 

59,2 10.000  *-m. 
+10,000=24,5°"      +81. 5  =726,500 1- 
WE.B8I  xf-,=35.4      +16000  =  45,40" 

£   Web  =  4,4 

3  Pis.  14x1=27,0 
45,3 

Length  of  Covers 
Top  —   Full,    47',  34" 
Bottom  -  57,  47;  34' 


STRINGERS 


INT.  FLOOR  BE  AM 


END  FLOOR  SEAM 


SHEAR 
D=    2,800 
L=  60,000 
1=57,200 

120,000 t 
+10,000  =l2,0a" 


MOMENT 
0=    103,000 
t=  1,980,000 
7r  1.892,000 

3,975, 000-Hn. 
±18,8=211,500* 
t      +13,000=    13.20" 

1  Web  -  1.7 

2  Ls6  x6  x  A-II.7 


SHEAR 
D=   6.800 
L=  78, 300 
I  =  71,600 

158, 700 1 
+10,000=15.7°" 
WEB  32x±  =/g,o 


MOMENT 
D=    347,000 
L  =  3,993,000 
1  =  3,652,000 

S,992,000*ln, 
•+28.7=878,500'* 
+16,000=       17.40" 
2.0 


SHEAR 
D=  3,400 
t=  57,900 
1=55,300 


116,600 

+10,000=11,70"  +27,0 
WEB  32xi=  12.0    +16.000= 


MOMENT 
D=      173,000 
L=  2,953.000 
1=  2,820,000 
5,  946,  000  tin. 
220,200*      , 


2  La  6  x  6  xi=!5.4 
17.4 


1.5 


14.5 


70  FT.   THRU 
PLATE  GIRDER  SPAN 

OVER  MILL  RIVER 

WOOD  BRIDGE  RAILROAD  CO. 

NEW  HAVEN,  CONN, 

UNIVERSITY  BRIDGE  COMPANY 


Fig.  21.    Typical  Design  Sheet. 


22 


PART  I  —  INTRODUCTORY 


order  to  reduce  the  number  of  members  to  be  shipped  and  to  be  erected 
at  the  site.  The  detailers  often  prefer  to  trace  their  own  drawings  or 
else  to  draw  with  ink  directly  upon  the  tracing  cloth,  thus  making  no 
use  of  the  tracers.  The  detailers  are  often  called  upon  either  to  make 
or  to  check  shop  bills  and  shipping  bills  and  other  lists  of  material. 
Most  of  the  billing  and  the  calculating  of  weights  are  done  by  younger 
men  of  limited  experience  often  working  in  a  separate  squad  under  a 
chief  biller.  The  checkers  "check  "  or  verify  the  drawings  and  indicate 
the  mistakes.  They  are  often  called  upon  to  make  drawings  also.  They 
are  men  of  greater  experience  than  the  detailers  and  they  assist  the 
squad  foreman  in  laying  out  new  work  preparatory  to  ordering  the 
material.  The  term  "draftsman  "  has  a  double  meaning.  Some  limit 
its  use  to  detailers  because  they  do  the  actual  drafting,  while  others 
refer  to  everyone  in  the  Drafting  Department  as  draftsmen,  particularly 
those  who  have  reached  or  passed  the  rank  of  detailer. 

1.  Method  of  Procedure.  —  When  a  new  contract  is  received  in  the 
Drafting  Department  the  Chief  Draftsman  studies  the  general  character 
of  the  structure,  notes  the  time  limit  if  any,  and  assigns  the  work  to  the 
squad  foreman  who  can  best  handle  it.  The  squad  foreman  makes  a 
careful  study  of  the  whole  contract  and  adopts  the  method  of  procedure 
by  which  the  work  under  his  direction  can  be  carried  out  most  effi- 
ciently. In  general  his  first  aim  is  to  have  all  main  material  ordered  as 
soon  as  possible  because  of  the  usual  delay  at  the  mills.  In  some  types 
of  structure  either  he  or  his  more  experienced  men  can  list  most  of  the 
material  directly  from  the  design  sheets.  In  certain  classes  of  work 
such  as  truss  work  it  may  become  necessary  to  make  small  layouts  of 
connections,  or  even  to  begin  the  working  drawings  in  order  to  deter- 
mine the  lengths  of  the  material;  later  these  preliminary  drawings  may 
be  given  to  detailers  for  completion.  In  other  types  of  structure  such 
as  office  buildings  it  may  prove  feasible  to  make  the  plans  and  diagrams 
before  listing  the  material.  These  diagrams  may  be  made  so  complete 
that  the  material  may  be  listed  from  them  quickly  and  accurately,  and 
the  detailed  drawings  may  become  routine  work  which  can  be  done  by 
men  of  limited  experience.  The  preliminary  lists  of  material  are  usu- 


ally sent  to  an  Order  Department  where  the  material  is  summarized 
and  the  short  pieces  are  grouped  in  multiple  lengths  to  be  cut  after  they 
arrive  from  the  mill.  The  squad  foreman  divides  the  drafting  among 
the  detailers  to  the  best  advantage  so  that  the  work  may  be  carried  on 
efficiently  and  in  logical  order.  Part  of  the  drawings  may  be  sent  to 
the  shop  before  all  are  completed  and  as  far  as  practical  an  attempt 
should  be  made  to  complete  the  drawings  in  approximately  the  same 
order  that  the  corresponding  members  will  be  erected.  For  example, 
the  drawings  of  the  ground  floor  beams  in  an  office  building  should 
be  made  before  the  drawings  of  the  roof  beams.  Erection  diagrams 
should  be  made  as  soon  as  possible  so  that  the  marks  of  all  members 
may  be  recorded  as  soon  as  determined.  Drawings  should  be  checked 
shortly  after  they  are  made  and  the  shop  bill  for  each  drawing  should 
be  made  as  soon  as  the  drawing  is  completely  checked.  A  shop  bill  is 
a  summary  of  all  the  material  required  to  make  all  the  members  repre- 
sented by  a  drawing.  Later  shipping  bills  and  lists  of  rivets  and  blots 
to  be  used  in  erection  are  prepared. 

2.  The  squad  foreman  should  keep  progress  sheets  so  that  he  and 
the  chief  draftsman  can  tell  what  has  been  done,  what  is  being  done, 
and  when  and  where  the   blueprints   have  been  issued.      He  should 
keep  separate  files  for  the  drawings  and  for  the  correspondence  of  each 
different  contract.     Usually  all  communications  pass  through  the  hands 
of  the  chief  draftsman  who  writes  all  letters  and  serves  as  intermediary 
between  the  men  in  the  drafting  room  and  those  outside.     A  detailed 
account  of  the  duties  of  the  draftsmen  appears  in  Parts  II  and  III. 

3.  There  should  be  greater  cooperation  between  the  engineering  de- 
partment and  other  departments  than  sometimes  exists.     Shop  men  and 
erectors  often  complain  of  points  in  the  design  or  the  details  of  a  mem- 
ber which  bother  them,  but  seldom  do  their  criticisms  reach  the  source 
of  the  trouble.     It  would  be  to  the  advantage  of  all  concerned  if  the 
erectors  and  the  shop  foremen  would  issue  periodical  bulletins  which 
would  reach  each  designer,  each  draftsman,  and  each   shop   foreman. 
Suggestions  and  constructive  criticisms  could  thus  be  presented   in  such 
a  manner  that  future  trouble  might  be  avoided. 


CHAPTER  III 
THE  MANUFACTURE   OF   STRUCTURAL  STEEL* 

SYNOPSIS:  This  topic  has  no  direct  bearing  upon  the  work  of  the  draftsman  but  he 
should  have  a  general  idea  of  how  steel  is  made.  It  is  important  that  he  know  the 
form  it  is  in  when  it  first  reaches  the  structural  company. 


1.  Iron.  —  Most  of  the  iron  ore  is  taken  from  open  pit  mines  in  the 
Lake  Superior  region  and  shipped  by  boat  and  by  rail  to  blast  furnaces 
where  it  is  smelted  or  reduced.  The  ores  are  oxides  of  iron  and  the  re- 
ducing agent  is  carbon.  A  blast  furnace  is  in  continuous  operation.  It 
is  charged  at  the  top  and  the  molten  iron  flows  by  gravity  to  the  bottom 
where  it  accumulates  until  tapped  at  intervals  of  about  6  hours.  Be- 
sides the  ore  the  charge  includes  a  flux,  and  the  reducing  agent  in  the 
form  of  coke  which  serves  also  as  fuel.  An  intense  heat  is  maintained 
by  means  of  a  continuous  hot  air  blast.  The  blast  is  heated  by  being 
passed  through  a  ''stove  "  lined  with  fire  brick.  Four  stoves  are  used 
in  turn,  the  ones  not  in  use  being  heated  by  the  hot  gases  from  the  fur- 
nace. Limestone  is  the  flux  commonly  used  to  unite  with  the  impurities 
freed  from  the  ore  to  form  a  fused  mass  called  "slag."  This  floats  on  top 
of  the  iron  and  is  tapped  at  a  higher  elevation.  The  iron  tapped  from 
a  blast  furnace  is  called  "  pig  iron  "  because  it  is  often  cast  into  "  pigs  "  of 
about  100  pounds  for  convenient  handling.  Pig  iron  is  used  in  iron 
foundries  for  making  iron  castings,  but  most  of  the  pig  iron  is  made  into 
wrought  iron  or  steel.  When  the  steel  furnaces  are  near  the  blast  fur- 
nace the  iron  may  be  transferred  in  the  molten  state  in  large  ladles.  Pig 
iron  contains  small  quantities  of  carbon  (3  to  4  per  cent),  silicon,  sulphur, 
phosphorous,  and  manganese.  It  has  so  much  carbon  that  it  is  not 

*  The  manufacture  of  iron  and  steel  is  treated  more  completely  in  many  books,  as 
for  example:  Stoughton's  "The  Metallurgy  of  Iron  and  Steel,"  McGraw-Hill  Book 
Co.  Inc.,  New  York;  Moore's  "Materials  of  Engineering,"  McGraw-Hill  Book  Co.  Inc., 
New  York;  or  Burt's  "Steel  Construction,"  American  Technical  Society,  Chicago. 


23 


malleable  at  any  temperature.     The  capacity  of  a  blast  furnace  is  about 
500  tons  of  iron  per  24  hours. 

2.  Structural  steel  is  made  by  the  "open  hearth  "  process.     A  higher 
grade  of  steel  for  tools  and  instruments  is  made  in  crucibles  or  in  electric 
furnaces.     At  first  structural  steel  was  made  by  the  Bessemer  process  in 
a  converter  of  from  10  to  20  tons  capacity.     A  cold  air  blast  was  used  for 
about  10  minutes  after  which  the  steel  was  ready  to  be  poured.     Besse- 
mer steel  is  inferior  in  quality  and  is  less  reliable  than  open  hearth  steel, 
and  the  Bessemer  process  has  been  largely  superceded  by  the  open  hearth 
process.     In  the  latter  the  charge  is  placed  on  a  shallow  hearth  and  sub- 
jected to  a  hot  air  blast.     The  charge  includes  besides  the  pig  iron,  iron 
ore,  steel  scrap,  and  usually  limestone.     Gas  is  used  for  fuel,  and  when 
the  charge  is  melted  the  flux  rises  to  the  top.     This  flux  contains  the  iron 
ore  which  forms  a  blanket  to  prevent  the  oxygen  of  the  air  from  com- 
bining with  the  iron.     The  impurities  in  the  iron  become  oxidized  by 
the  iron  ore  which  in  turn  receives  new  oxygen  from  the  air.     The  per- 
centage of  carbon  and  phosphorus  is  thus  reduced.     The  steel  is  tapped 
into  large  ladles  where  it  is  "  recarbonized  "  by  adding  the  proper  amount 
of  carbon  and  other  ingredients  to  give  the  desired  quality.     Structural 
steel  contains  from  0.15  to  0.3  per  cent  of  carbon.     The  capacity  of  an 
open  hearth^furnace  is  from  30  to  70  tons,  and  the  operation  requires 
from  6  to  10  hours. 

3.  Rolling  the  Steel.  —  From  the  ladles  the  steel  is  poured  into  ingot 
molds  and  allowed  to  cool  until  sufficient  crust  is  formed  to  permit 
handling.     The  molds  are  then  stripped  off  and  the  ingots  are  placed  in 


24 


PART  I  —  INTRODUCTORY 


ovens  called  "soaking  pits"  until  the  inside  portion  solidifies  and  the 
whole  becomes  of  the  proper  uniform  temperature  for  rolling.  Structural 
shapes  are  formed  by  passing  the  material  between  rolls  of  the  proper 
shape,  the  cross  section  being  reduced  and  the  piece  elongated  at  each 
pass.  The  ingot  is  first  passed  between  the  two  cylindrical  rolls  of  a 


Fig.  24  (a).   Typical  Roughing  Rolls  for  an  I-beam. 
(Courtesy  of  the  Pittsburgh  Rolls  Corporation.) 

"blooming  mill"  and  flattened.  The  rolls  are  then  reversed  and  placed 
closer  together  and  the  material  is  passed  between  them  in  the  opposite 
direction.  In  this  manner  slabs  are  made  of  suitable  size  to  be  placed 
in  another  mill  to  be  rolled  into  plates.  For  other  shapes,  the  ingot  is 
rotated  at  right  angles  between  successive  passes  to  form  a  "bloom"  of 
the  size  best  adapted  to  the  shape  of  the  "roughing  rolls."  The  blooms 
are  cut  into  lengths  which  will  result  in  the  proper  lengths  of  the  final 


sections.  The  roughing  rolls  are  grooved  to  work  the  blooms  down  gradu- 
ally to  shapes  which  approximate  the  finished  pieces,  then  "finishing 
rolls"  are  used.  Both  the  roughing  and  finishing  rolls  are  so  shaped  that 
at  each  pass  the  material  is  reduced  in  cross  section  to  approach  the 
finished  shape.  These  rolls  are  "three  high  "  so  that  they  need  not  be 
reversed,  the  material  passing  alternately  between  the  lower  two  in  one 


HUH  14 1 


Fig.  24  (6).   Typical  Finishing  Rolls  for  an  Angle. 
(Courtesy  of  the  Pittsburgh  Rolls  Corporation.) 

direction  and  the  upper  two  in  the  opposite  direction.  Typical  roughing 
rolls  for  an  I-beam  are  illustrated  in  Fig.  24  (a),  and  finishing  rolls  for  an 
angle  in  Fig.  24  (6).  The  material  is  handled  on  roller  platforms  on  both 
sides  of  the  rolls.  These  platforms  may  be  raised  or  lowered  to  receive 
the  steel  at  one  elevation  and  deliver  it  at  another.  The  material  may  be 
moved  longitudinally  by  means  of  the  rollers,  and  transversely  by  means 
of  arms  between  the  rolls.  The  whole  operation  is  controlled  electrically. 


CHAPTER  III 


THE  MANUFACTURE  OF  STRUCTURAL  STEEL 


25 


1.  The  Effect  of  Spreading  the  Rolls.  —  The  finishing  rolls  are  kept 
at  a  fixed  distance  apart  during  the  rolling.     When  they  are  spaced  at 

the  minimum  dis- 
tance the  lightest 
section  of  a  group  is 
made.  When  the 
rolls  are  spaced 
farther  apart  heav- 
ier sections  are 
made,  as  indicated 
in  Fig.  25  (a).  The 
effect  of  spreading 
the  rolls  is  to  in- 
the  web 


Fig.  25  (a).   The  Method  of  Enlarging  Cross  Sections  by 
Spreading  the  Rolls. 

crease 

thickness  and  the  flange  width  of  an  I-beam  or  channel  without  changing 
the  depth.      The  variations  are  indicated   in  the  tables.      Angles  of 
different  thicknesses  may  be  rolled  in  the  same  mill  but  from  Fig.  25  (a)  it 
is  apparent  that  as  the  rolls  are  separated  the  lengths  of  the  legs  as 
well  as  the  thickness  will  be  increased.     The  tables  of  this  book  con- 
form to  the  usual  practice  and  indicate  only  the  nominal  lengths  of 
legs.     Since  the  nominal  size  is  the  size  only  of  the  thinnest  section 
of  a  group,  the  draftsman  should  take  care  to  allow  ample  clearances 
for  the  overrun  of  the  thicker  angles.     The  increase  in  the  length  of 
the  leg  is  equal  to  the  increase  in  thickness.     On  account  of  this 
variation  and  also  because  of  the  wearing  of  the  rolls  and  of  the  in- 
accuracies in  setting  them,  the  lengths  of  angle  legs  and  the  widths  of 
I-beam   and   channel  flanges  are  indefinite;    dimensions  should  be 
referred  to  the  backs  of  angles  and  channels  and  to  the  center  lines 
of  I-beams  rather  than  to  the  rolled  edges. 

2.   Mill  Variation.  —  Structural  shapes  other  than  plates  are  sawed 
to  the  ordered  lengths  as  soon  as  they  leave  the  finishing  rolls,  while  still 
red  hot.     They  must  be  measured  and  sawed  into  the  proper  number 
of  pieces  before  the  following  piece  leaves  the  rolls,  and  extreme  accuracy 
cannot  be  assured.     The  usual  "mill  variation  "  is  plus  or  minus  f  of  an 
inch,  and  drawings  should  be  so  made  that  I-beams  and  channels  par- 
ticularly can  be  used  without  being  recut  in  the  shop.     In  view  of  this 


variation,  the  mill  orders  should  be  given  in  lengths  which  are  multiples 
of  \  inch  and  preferably  \  inch.  The  maximum  length  varies  with  the 
size  from  50  to  90  feet.* 

3.  Plates  may  be  rolled  in  a  mill  with  horizontal  rolls  only,  or  in  a 
Universal  Mill  which  has  vertical  as  well  as  horizontal  rolls.  The  hori- 
zontal rolls  are  brought  closer  together  between  successive  passes  of  the 
plate  until  the  desired  thickness  is  reached.  At  each  pass  the  length  is 
increased,  and  unless  vertical  rolls  are  used  the  width  also  is  increased. 
"Universal  Mill"  plates  or  "edged  plates"  having  rolled  edges  are 
rolled  up  to  48  inches  in  width  and  in  some  sizes  up  to  100  feet  in  length.* 
All  other  plates  have  to  be  sheared  to  the  desired  width  and  they  are 
termed  "sheared  plates."  These  are  rolled  up  to  132  inches  in  width 
and  the  lengths  vary  inversely  with  the  width  from  15  to  47  feet.*  Uni- 
versal Mill  (UM)  plates  are  used  chiefly  for  the  cover  plates  of  bridge 
girders;  sheared  plates  aft  used  for  most  other  work.  Sheared  plates  are 
usually  furnished  unless  Universal  Mill  plates  are  specified.  Plate 
thicknesses  vary  by  sixteenths  of  an  inch  from  f\  to  2  inches,  the  usual 

Width  of  Flange 


12 


- 1=  Thickness 
of  Web 


Radius  of  Fillet  ~t+0.l" 

e  as  t  except 
20"and  241s. 


Radius -Q. 8  t 
Radius  of  Fillet=t+0.l" 


-f=  Thickness 
of  Well 


12 


ANGLE 


I-BEAM  CHANNEL 

Fig.  25  (6).     Actual  shapes  of  cross  sections. 


range  in  structural  work  being  from  -fa  to  1  inch  except  for  fillers  and 
bearing  plates.     Any  width  of  plate  may  be  sheared  from  larger  sizes, 

*  See  tables  of  extreme  lengths  in  Ketchum's  "Structural  Engineers'  Handbook," 
McGraw-Hill  Book  Co.  Inc.,  New  York. 


26 


PART  I  —  INTRODUCTORY 


but  the  draftsman  should  attempt  to  use  widths  without  fractions,  and 

if  over  24  inches  in  multiples  of  2  inches.  The 
reason  for  this  is  to  reduce  the  number  of  differ- 
ent sizes,  which  expedites  the  filling  of  an  order 
at  the  mill  and  simplifies  the  maintenance  of  a 
serviceable  plant  stock. 

1.  The  actual  shapes  of  the  cross  sections  of 
the  angle,  the  standard  I-beam,  and  the  channel 
are  shown  in  Fig.  25  (6).  Plates,  and  round  and 


TEE 


Z-BAR, 


Fig.  26. 


square  rods  need  not  be  illustrated.     Shapes  used  less  commonly  than 


formerly  are  shown  in  Fig.  26.  The  proportions  of  rails  are  shown  on 
page  317.  Curves  are  introduced  to  facilitate  rolling.  These  curves 
are  disregarded  in  computing  the  areas  of  cross  section  and  the  weights 
per  foot  of  length.  The  curves  are  not  shown  in  the  usual  structural 
drawings,  but  the  draftsman  must  constantly  bear  in  mind  their  existence 
and  make  proper  allowance.  This  is  especially  important  in  the  places 
where  the  introduction  of  curves  results  in  the  use  of  more  metal  rather 
than  less,  as  for  example  at  the  junction  of  the  flanges  and  the  web.  Such 
additional  metal  is  termed  a  "fillet "  and  it  serves  also  to  reinforce  the 
web  at  critical  points. 


CHAPTER  IV 
THE  FABRICATION   OF   STRUCTURAL  STEEL 

SYNOPSIS:  This  outline  of  the  shop  operations  of  a  structural  company  is  given 
primarily  for  students.  A  more  thorough  knowledge  gained  from  observation  is  essen- 
tial to  draftsmen. 


1.  In  order  to  make  working  drawings  intelligently,  it  is  necessary 
that  a  person  have  a  very  definite  conception  of  their  purpose  and  of  the 
use  to  be  made  of  them.     To  those  who  have  had  no  opportunity  to  gain 
this  knowledge  this  chapter  gives  an  abstract  of  the  more  important  steps 
taken  in  preparing  or  "fabricating  "  the  steel  for  erection.     The  term 
"  fabrication  "  is  interpreted  to  include  all  the  shop  work  necessary  to  lay 
out,  cut,  punch,  assemble,  and  rivet  into  complete  members,  the  steel 
shapes  as  they  come  from  the  rolling  mills.     In  general  the  steel  shapes 
are  handled  cold  during  fabrication  in  contrast  to  their  being  heated  at 
the  steel  mills.     A  member  may  be  a  single  piece  as  a  beam  or  an  angle, 
or  it  may  be  composed  of  many  pieces  as  a  girder  or  a  truss.     Shop  work 
is  preferred  to  field  work  because  of  better  facilities;  the  work  at  the  site 
should  be  reduced  as  much  as  practical  considering  the  limits  in  the  size 
of  members  due  to  the  requirements  of  shipment  and  erection. 

2.  Only  the  more  elementary  points  can  be  mentioned  here,*  but 
students  or  others  who  seek  employment  as  draftsmen  must  make  a 
careful  study  of  shop  methods.     It  is  sufficient  for  the  more  observing 
men  to  make  frequent  trips  to  the  shop  outside  of  their  office  hours, 
cultivating  the  habit  of  learning  something  new  at  each  trip  even  in  short 
visits  during  the  noon  hour.     Many  men  wander  blindly  through  the 
shop  day  after  day  without  tangible  results.     For  them  a  limited  period 

*  See  also  Thayer's  "Structural  Design,"  Vol.  I,  D.  Van  Nostrand  Co.,  New  York; 
Merriman  and  Jacoby's  "Roofs  and  Bridges,"  Vol.  Ill,  John  Wiley  and  Sons,  Inc., 
New  York;  or  Well's  "Steel  Bridge  Designing,"  The  McGraw-Hill  Book  Co.  Inc., 
New  York. 


of  shop  work  or  field  work  in  the  capacity  of  timekeeper  may  prove 
beneficial. 

3.  Shop  methods  are  to  a  certain  extent  dependent  upon  the  size  of  the 
company,  its  equipment,  and  the  nature  of  its  output.     In  general  most 
of  the  drawings  are  first  used  in  the  templet  shop  and  then  in  the  struc- 
tural shop.     In  some  cases,  such  as  simple  beam  work,  the  measurements 
may  be  laid  out  in  the  structural  shop  directly.     Drawings  for  special 
work,  such  as  eye  bars,  castings,  rollers  and  pins,  and  forgings,  are  sent 
directly  to  the  eye-bar  shop;  to  the  pattern  shop  and  foundry,  to  the 
machine  shop,  or  to  the  forge  shop.     Some  companies  are  not  equipped 
to  handle  all  of  this  work  but  have  it  done  elsewhere  when  occasion  arises. 

4.  The  plant  layout  should  be  such  that  the  material  may  pass  from 
the  receiving  or  stock  yard  to  the  shipping  yard  through  the  different 
operations  with  the  least  movement.     The  different  machines  should  be 
arranged  so  that  the  material  may  pass  from  one  to  the  other  in  logical 
order  without  interference.     The  material  is  handled  by  overhead  travel- 
ing cranes,  jib  cranes,  gantry  cranes,  small  hoists,  derricks,  or  small 
trucks  or  cars  on  narrow-gage  or  standard-gage  tracks. 

5.  In  the  templet  shop  ''templets  "  are  made  for  the  component  parts 
of  almost  all  plate  and  angle  work  and  for  some  I-beams  and  channels. 
The  templets  are  wooden  strips  or  skeleton  frames  made  of  strips,  upon 
which  are  shown  the  location  of  all  holes  and  cuts.     They  are  usually 
made  from  f  "  or  f "  planed  pine  boards.     Templets  for  angles  are  made 
of  one  or  two  strips.     (See  Fig.  28  (a)  and  (6).)     The  single  strip  may  or 
may  not  be  the  same  width  as  the  corresponding  angle  leg,  but  transverse 


27 


28 


PART  I  —  INTRODUCTORY 


distances  must  be  measured  from  the  edge  of  the  strip  which  will  be 
placed  at  the  vertex  of  the  angle.  The  positions  of  all  holes  for  shop  or 
field  rivets  are  carefully  laid  out  on  the  templet  and  holes  \"  in  diameter 
are  bored  in  the  wood  through  which  the  centers  are  indicated  on  the 
steel  by  means  of  a  "  center  punch."  When  holes  are  to  be  punched  in 
both  legs  of  an  angle  one  strip  may  be  used  for  both  or  the  templet  may 
be  made  of  two  strips  fastened  together  at  right  angles  to  fit  over  the 
steel  angle.  Distances  are  measured  from  the  inner  vertex  to  correspond 
to  distances  on  the  angle  which  are  measured  from  the  outer  vertex. 
One  strip  must  be  full  length  but  the  other  may  be  made  of  one  or  more 
short  pieces  instead  of  full  length  if  the  number  of  holes  is  small.  When 
angles  are  made  in  pairs,  i.e.,  rights  and  lefts  (page  81 :  2)  as  stiffening 
angles  or  flange  angles,  a  T-shaped  templet  is  made.  See  Fig.  28  (c). 

One-half  is  used  for  one 
1  angle  and  the  other  half 
for  the  other  angle,  the 
holes  in  the  stem  serving 
for  one  leg  of  each  angle. 
For  small  plates  full  sized 
templets  are  used,  but 
for  large  plates  rigid  frames  are  made  from  strips  of  wood  in  order  to 
save  lumber  and  to  facilitate  handling.  Parallel  strips  may  be  used 
for  the  holes  along  the  edges  of  a  plate,  cross  strips  being  inserted 
wherever  intermediate  holes  are  required.  Sufficient  diagonals  are 
added  to  prevent  distortion.  For  small  connection  or  "gusset  "  plates 
templets  are  often  made  of  cardboard.  This  is  more  easily  cut  and 
punched  than  wood  and  it  is  sufficiently  durable  to  be  used  many 
times.  For  I-beams  and  channels  several  types  of  templets  may  be 
used.  For  the  flanges  strip  templets  may  be  used  if  the  number  of 
similar  pieces  justifies  their  use;  otherwise  the  holes  are  laid  out  di- 
rectly on  the  steel.  The  holes  in  the  web  may  be  (1)  laid  out  on  the  steel, 
(2)  laid  out  on  full  length  templets,  or  (3)  laid  out  in  groups  on  separate 
templets  which  are  located  by  direct  measurement.  The  third  scheme  is 
well  adapted  to  the  use  of  standard  connections,  for  the  group  templets 
may  be  used  repeatedly  for  different  contracts.  In  order  to  economize 
lumber  and  to  reduce  the  number  of  templets  to  be  handled  and  stored, 


w 

Fig.  28.   Templets  for  Angles. 


one  templet  may  often  be  made  for  pieces  which  are  not  identical.  The 
pieces  must  be  similar  even  though  of  different  length,  and  most  of  the 
holes  must  be  in  the  same  relative  position  although  not  all  of  the  holes 
need  be  punched  in  every  piece.  Special  marks  and  notes  are  painted  on 
the  templets  to  indicate  which  cuts  and  which  holes  are  to  be  used  for 
each  piece.  The  contract  number,  the  drawing  number,  the  size  of  the 
holes,  the  identification  mark,  and  the  number  of  pieces  required,  are 
painted  on  each  templet.  Since  the  detailed  dimensions  of  a  working 
drawing  are  used  chiefly  by  templet  makers,  the  draftsmen  should  pay 
particular  attention  to  their  needs. 

1.  The  Stock  Yard.  —  As  the  steel  arrives  from  the  rolling  mill  it  is 
unloaded  in  the  receiving  yard  or  stock  yard  by  overhead  cranes.  Usu- 
ally enough  material  of  different  shapes  is  kept  in  the  stock  yard  for  the 
details  and  other  parts  which  cannot  be  included  in  the  original  mill 
orders.  Material  required  on  account  of  changes  or  additions  to  a  struc- 
ture may  often  be  provided  in  this  way  without  delay.  Most  of  the 
material  for  each  contract  is  ordered  specially  for  that  contract  and  it  is 
held  in  the  receiving  yard  until  required.  Since  much  of  the  material  is 
ordered  in  multiple  lengths,  particularly  plates  and  angles,  it  must  be  cut 
to  dimension.  This  is  usually  done  in  the  receiving  yard  or  in  the  .re- 
ceiving end  of  the  structural  shop  from  the  "shop  bills  "  upon  which  the 
required  material  is  summarized.  Plates  and  angles  are  cut  cold  by 
shearing,  each  by  a  single  stroke.  The  plate  shear  has  one  fixed  hori- 
zontal blade  and  one  movable  blade  which  moves  in  a  vertical  plane. 
One  end  of  the  movable  blade  is  slightly  lower  than  the  other  so  as  to 
cut  the  plate  gradually  instead  of  the  whole  width  at  once.  The  cutting 
edge  of  the  upper  blade  is  placed  so  it  will  just  clear  the  cutting  edge  of 
the  lower  blade  much  as  the  two  blades  of  ordinary  scissors  are  arranged. 
Angle  shears  cut  both  legs  at  once,  one  leg  being  placed  against  a  hori- 
zontal cutting  edge  and  the  other  against  a  vertical  one.  A  single  knife 
with  two  cutting  edges  moves  diagonally  past  these  two.  Diagonal  cuts 
on  plates  and  angles  may  be  made  by  running  in  the  material  obliquely 
or  by  rotating  the  shears  horizontally.  I-beams  and  channels  are  usually 
ordered  from  the  mill  in  the  desired  lengths  because  the  flanges  prevent 
them  from  being  cut  as  simply  as  plates  and  angles.  Special  beam  shears 
are  made  which  cut  first  one  flange  and  then  the  other  but  nearly  an  inch 


an  mcu 


CHAPTER  IV 


THE   FABRICATION   OF  STRUCTURAL  STEEL 


29 


of  material  is  wasted  at  each  cut.  Circular  "cold  saws  "  are  also  used 
for  sawing  beams,  especially  the  heavier  ones  and  those  with  diagonal 
cuts.  The  oxy-acetylene  flame  is  sometimes  used  when  shears  cannot 
be  used  advantageously. 

1.  Some    of    the    material    becomes    bent    during    shipment,    par- 
ticularly the  plates.     Before  they  can  be  used  in  the  shop  they  must 
be  straightened   by   being    passed    between   a  series   of    straightening 
rolls. 

2.  The  first  step  in  the  fabrication  of  riveted  work  after  the  material 
is  cut  to  length  is  the  "  laying  out."     This  includes  the  marking  of  the 
steel  from  the  templets  when  templets  are  used,  and  also  the  laying  out 
on  the  steel  directly  from  the  drawings  when  templets  are  not  used.     The 
wooden  templets  are  clamped  in  the  proper  position  on  the  steel  and  all 
notches  and  special  cuts  are  marked  with  a  piece  of  soapstone.     The 
centers  of  holes  are  indicated  by  small  dents  in  the  steel.     These  dents 
are  made  by  placing  a  "center  punch  "  through  the  \"  holes  of  the 
templets  and  striking  the  top  of  it  with  a  hammer.     The  center  punch  is 
slightly  smaller  than  the  hole  in  the  wood  so  that  it  can  be  centered 
easily,  and  a  short  sharp  point  protrudes  from  the  end  for  making  the 
dent.     The  soapstone  marks  which  indicate  the  cuts  are  made  more 
permanent  by  a  series  of  center  punch  marks.     White  paint  is  used  to  call 
attention  to  the  presence  of  all  marks  which  might  otherwise  be  over- 
looked.    The  contract  number,  the  identification  mark,  the  sheet  number 
of  the  corresponding  drawing,  and  the  size  of  the  holes  are  also  painted 
on  the  steel,  the  first  two  being  painted  on  at  the  mill  or  in  the  yard 
where  the  material  is  cut  to  length. 

3.  Coping.  —  Corners  of  plates  and  angles  may  be  cut  off  by  the 
shears  already  described.     Notches  may  be  cut  with  special  "blocking 
out  "  punches  or  by  punching  a  series  of  circular  holes  and  then  smooth- 
ing the  rough  edges  with  a  pneumatic  chisel.     Reentrant  angles  in  plates 
should  be  avoided  for  they  are  difficult  and  expensive  to  make.     I-beams 
and  channels  are  coped  and  notched  in  a  special  coping  machine  or  by 
means  of  an  oxy-acetylene  flame.     A  beam  is  "coped  "  at  the  end  to 
clear  the  flange  of  a  beam  to  which  it  connects.     First  the  flange  is 
blocked  out  and  then  the  web  is  cut.     Coping  requires  two  or  three 
strokes;  some  machines  block  out  only  one  side  of  the  flange  of  an  I-beam 


at  a  stroke  while  others  cut  both  sides.     The  flanges  may  be  blocked  out 
on  one  side  only  if  desired. 

4.  Other  preliminary  operations  may  be  required  in  shaping  the  com- 
ponent parts  of  a  member  before  they  can  be  assembled.     For  example, 
the  ends  of  "stiffening  angles  "  which  are  to  be  placed  against  the  inner 
faces  of  other  angles  must  be  rounded  to  allow  for  the  curved  fillets  of  the 
second  angles  (page  96  :  1).     This  may  be  effected  (1)  by  grinding,  (2)  by 
planing,  or  (3)  by  chamfering  with  rotating  cutters.     When  a  stiffening 
angle  is  "crimped  "  or  offset  for  one  leg  of  the  angle  against  which  it  is 
to  rest,  as  shown  in  section  BB,  Fig.  102,  it  must  be  taken  to  the  forge  shop 
and  bent  while  hot.     Plates  or  other  shapes  occasionally  have  to  be  planed 
on  the  edges,  and  some  plates  must  be  planed  on  one  side  to  insure  a 
uniform  bearing  surface.     A  small  cutting  tool  is  made  to  pass  across  the 
surface  repeatedly  thus  cutting  a  series  of  thin  narrow  strips  until  the 
desired  depth  or  area  is  planed. 

5.  Punching.  —  Holes  may  be   punched,   drilled,   or   bored.     Rivet 
holes  are  usually  punched  to  the  desired  size  by  "punches."     The  shape 
of  the  punch  and  the  corresponding  die  is  shown  in  Fig.  29. 

The  punch  housing  is  stationary;  the  steel  to  be  punched  is 
moved  with  the  aid  of  a  small  hoist  until  the  dent  which  in- 
dicates the  location  of  a  hole  is  directly  below  the  small 
projection  on  the  punch  shown  in  the  figure;  the  punch  is 
then  released  and  it  passes  through  the  metal.  Most  holes 
"are  single  punched,"  i.e.,  punched  one  at  a  time,  but  the 
larger  plants  are  equipped  with  some  form  of  multiple 
punch,  in  which  any  or  all  of  the  punches  can  be  released 
at  once.  For  example,  multiple  punches  are  used  for  punching  groups 
of  holes  for  standard  connections  in  beams,  and  also  for  punching 
the  holes  in  web  plates  and  cover  plates.  In  conjunction  with  the 
latter  a  spacing  rack  is  sometimes  used  which  can  be  set  and  used  in 
advancing  the  plate  to  correspond  to  the  desired  rivet  spacing.  Special 
racks  are  sometimes  used  in  conjunction  with  an  ordinary  punch  for 
duplicating  connection  plates.  The  holes  are  first  laid  out  on  one  plate 
and  punched,  then  this  plate  is  clamped  in  the  rack  under  an  indicator. 
A  blank  plate  of  the  same  form  is  clamped  in  the  rack  in  such  a  position 
that  the  punch  is  in  the  same  relative  position  as  the  indicator  of  the  first 


Fig.  29. 


30 


PART  I  —  INTRODUCTORY 


plate.  The  rack  is  moved  until  the  indicator  falls  into  a  hole,  then  the 
punch  is  released  and  a  corresponding  hole  is  made  in  the  second  plate. 
Obviously  no  benefit  is  derived  from  a  multiple  punch  unless  it  can  be 
used  many  times  with  each  setting. 

1.  Drilling.  —  Rivet  holes  are  also  drilled.     In  some  of  the  highest 
class  of  work  drilled  holes  are  specified  for  they  may  be  made  true  cylin- 
ders, accurately  centered,  with  less  damage  to  the  surrounding  metal 
than  punched  holes.     Holes  for  important  field  connections  are  often 
drilled  in  both  connecting  parts  through  the  same  metal  templet  so  that 
they  will  match  exactly.     Sometimes  connecting  members  are  held  to- 
gether in  the  proper  relative  position  and  the  holes  are  then  drilled 
through  both  members  at  once  to  insure  a  perfect  connection.     Holes 
are  also  drilled  in  metal  which  is  too  thick  to  be  punched.     In  general 
holes  may  be  punched  in  metal  as  thick  as  the  diameter  of  the  punch,  but 
it  is  difficult  to  prevent  the  punches  from  bending  when  the  metal  is 
thicker.     Many  specifications  state  that  no  holes  shall  be  punched  in 
metal  thicker  than  f ".     Fixed  drill  presses  are  used  for  small  pieces  such 
as  base  plates  which  are  moved  into  position  under  the  drills.     Radial 
drills  may  be  moved  radially  in  an  arm  which  can  be  swung  about  a 
vertical  axis.     Gang  drills  are  used  in  some  plants  for  drilling  a  large 
number  of  holes  in  heavy  members;  these  are  groups  of  radial  drills 
mounted  in  a  gantry  frame  which  passes  over  the  material  to  be  drilled. 

2.  Sub-punching.  —  Since  holes  in  connecting  parts  are  not  always  in 
perfect  alignment,  and  since  drilled  holes  are  much  more  expensive,  the 
holes  in  first  class  work  are  often  sub-punched  and  reamed.     The  holes 
in  each  component  part  are  punched  about  j"  smaller  than  the  desired 
diameter,  then  after  the  parts  are  assembled  pneumatic  reamers  are  used 
to  ream  out  the  holes  to  the  proper  size. 

3.  Assembling.  —  After  the  component  parts  of  a  member  are  ready 
they  are  assembled  by  "fitters"  and  held  in  position  by  shop  bolts. 
These  bolts  are  usually  longer  than  necessary,  enough  washers  being 
used  under  the  nuts  to  save  time  in  tightening  them.     At  least  two  bolts 
are  used  in  each  piece  to  keep  it  from  twisting. 

4.  Riveting,  —  The  assembled  members  are  next  taken  to  the  riveters 
who  drive  the  red  hot  "shop  rivets."     These  rivets  may  be  driven  (1)  by 
fixed  hydraulic  or  compressed  air  riveters,  (2)  by  movable  compressed  air 


riveters  or  "riveting  bulls"  such  as  shown  in  Fig.  30  (a),  (3)  by  pneumatic 
hammers  shown  in  Fig.  30  (6),  or  (4)  by  sledges.     Each  rivet  is  made  with 

one  head;  the  other  head  is  formed 
after  the  rivet  is  put  into  position. 
The  diameter  of  the  hole  is  made 
about  TV"  larger  than  the  diameter 
of  the  shank  of  the  rivet,  so  that 
the  rivet  can  be  inserted  more  easily; 
when  a  rivet  is  properly  "  driven " 
the  new  head  should  be  well  formed 
and  centered  and  the  shank  should 
be  "upset"  to  fill  the  hole.  The 
rivets  driven  by  machine  are  worth 
more  than  those  driven  by  hammer 
because  the  enormous  pressure 
(sometimes  100  tons)  is  sufficient 
not  only  to  form  good  heads  and  to 
upset  the  shanks  completely,  but  to 
bring  and  hold  the  component  parts 
in  perfect  contact  while  the  rivets 
are  being  set.  Some  "  fixed  "  riveters 
can  be  raised  or  lowered  to  drive 
rivets  in  girders  and  similar  mem- 
bers at  different  elevations  as  the  members  are  moved  along.  Perhaps 
the  majority  of  rivets  are  driven  by  movable  riveters,  either  the  member 


Fig.  30  (a).   Riveting  Machine. 

(Courtesy  of  the  Vulcan  Engineering 

Sales  Company.) 


Fig.  30  (6) .   Pneumatic  Hammer. 
(Courtesy  of  the  Chicago  Pneumatic  Tool  Company.) 

or  the  riveter  being  moved  as  is  most  convenient.     Air  hammers  or 
sledges  are  used  for  driving  rivets  which  are  inacessible  to  the  other 


CHAPTER  IV 


THE  FABRICATION  OF  STRUCTURAL  STEEL 


31 


forms  of  riveters.  When  hammers  are  used,  the  rivets  are  held  in  place 
by  "dolly  bars  "  either  of  pneumatic  type  or  simply  bent  rods  with  cup- 
shaped  ends  to  fit  the  rivet  heads.  Countersunk  and  flattened  rivets 
are  driven  by  the  same  methods  by  substituting  flat  dies  for  those  which 
form  the  "button  heads  "  of  the  ordinary  rivets.  Holes  for  countersunk 
rivets  are  reamed  by  special  reaming  tools  placed  in  the  drill  presses 
or  in  the  pneumatic  reamers.  Projecting  portions  of  countersunk  rivet 
heads  may  be  chipped  off,  if  necessary,  by  means  of  a  cutting  tool  or 
chisel  placed  in  the  pneumatic  hammer. 

1.  Milling.  —  The  ends  of  members  which  are  expected  to  transmit 
stress  by  direct  bearing  must  be  "planed,"  "faced,"  or  "milled."     This 
is  done  by  means  of  a  "  milling  machine  "  or  "rotary  planer  "  which  has 
numerous  cutters  arranged  near  the  edge  of  a  circular  cutting  head.     As 
the  head  slowly  rotates  it  advances  across  the  end  of  the  member.     Un- 
like the  teeth  of  a  saw,  the  cutters  are  set  in  the  plane  face  of  the  head 
toward  the  member  to  be  cut  instead  of  in  the  periphery,  and  it  is  im- 
portant that  they  project  equal  distances  from  the  face.     The  member  is 
clamped  in  front  of  the  planer  and  the  latter  can  be  turned  horizontally 
to  cut  the  member  at  the  proper  angle.     Milling  machines  are  often  used 
in  pairs  so  that  both  ends  of  a  member  may  be  faced  at  once. 

2.  Boring.  —  Holes  for  the  pins  of  pin-connected  structures  are  bored 
by  large  boring  machines.     These  are  often  arranged  in  pairs  so  that  the 
holes  at  each  end  may  be  bored  simultaneously  at  the  proper  distance 
apart.     The  holes  are  usually  roughed  out  by  punching  either  a  large 
hele  or  a  series  of  small  ones,  so  that  the  shaft  which  holds  the  cutter  may 
pass  through.     The  cutter  of  the  boring  machine  then  enlarges  the  hole 
to  the  proper  size. 

3.  Inspection.  —  Each  member  is  inspected  when  the  shop  work  is 
completed.     The  inspector  checks  the  important  measurements  and  the 
field  connections.     He  makes  sure  that  every  connection  is  provided  for, 
and  in  general  that  the  member  is  complete  and  properly  made.     He 
tests  the  rivets  with  a  hammer  and  rejects  any  loose  ones. 

4.  Painting.  —  One  or  more  coats  of  paint  or  oil  are  applied  to  each 
member  before  it  is  shipped.     Surfaces  whieh  are  inaccessible  for  paint- 
ing after  the  member  is  completed  are  given  one  coat  of  paint  before  the 
parts  are  assembled. 


5.  Shipping.  —  Most  members  are  first  shipped  by  rail  on  open  cars. 
They  are  loaded  to  the  best  advantage,  the  larger  members  being  sepa- 
rated by  wooden  blocks  to  prevent  damage  during  shipment.     Long 
girders  and  chords  may  extend  over  two  or  three  flat  cars  but  they  must 
be  so  mounted  that  they  will  not  interfere  with  the  passage  of  the  train 
around  curves.     Many  of  the  smaller  loose  pieces  are  bolted  to  larger 
members  for  shipment  in  accordance  with  notes  on  the  drawings;  others 
are  wired  together  or  boxed. 

6.  Other  operations  are  required  to  supplement  those  just  described. 
Some  plants  are  fully  equipped  while  others  have  much  of  the  miscellane- 
ous work  done  elsewhere.     Among  the  most  important  departments  may 
be  mentioned  the  machine  shop,  the  forge  shop,  the  foundry,  the  pattern 
shop,  the  eye-bar  shop,  and  the  bolt,  nut,  and  rivet  shop.     The  machine 
shop  provides  for  repairs  and  shop  maintenance  as  well  as  for  the  special 
machine  work  required  in  the  structures  made  for  the  customers.     Here 
the  various  tools  are  sharpened  and  kept  in  good  condition,  and  often 
some  tools  are  made.     Pins,  rollers,  and  turned  bolts  are  made  in  the 
machine  shop,  bed  plates  are  planed,  and  castings  are  drilled  and  finished 
there.     In  the  forge  shop  angles  and  other  shapes  are  bent,  rods  are  upset 
at  the  ends  to  neutralize  the  effect  of  thread  cutting  so  that  the  full  cross 
section  of  the  rods  will  be  developed,  and  loop  rods,  clevises,  turnbuckles, 
etc.,  are  made.     In  the  foundry  all  steel  and  iron  castings  are  made,  as 
for  example,  column  bases,  bridge  pedestals,  and  beveled  washers.     Pat- 
terns are  used  in  making  sand  molds  into  which  the  molten  iron  or  steel 
is  poured.     Patterns  are  made  in  a  pattern  shop  by  pattern  makers  not 
by  templet  makers  for  they  require  an  entirely  different  class  of  work- 
manship.    Patterns  are  models  of  the  finished  castings,  made  carefully 
to  scale.     They  are  made  larger  than  the  castings  by  the  use  of  "shrink- 
age scales  "  to  allow  for  the  shrinking  of  the  metal  while  cooling.     In  the 
eye-bar  shop  the  ends  of  eye  bars  are  upset  in  large  hydraulic  presses 
which  form  the  heads.     The  pin  holes  are  then  punched  and  later  bored 
to  the  proper  size.     The  bars  are  then  annealed,  i.e.,  heated  and  allowed 
to  cool  slowly  in  order  to  restore  the  uniform  properties  of  the  steel  before 
the  ends  were  heated  and  upset.     Rivets  and  bolts  are  made  from  heated 
rods  in  special  rivet  and  bolt  upsetting  machines.     Nuts  are  punched 
from  flat  bars.     After  the  bolts  and  nuts  are  cool  they  are  threaded.     The 


32 


PART  I  —  INTRODUCTORY 


separate  departments  mentioned  in  this  paragraph  are  referred  to  as 
"shops"  but  they  do  not  necessarily  require  separate  buildings.  For 
example,  the  pattern  shop  and  the  templet  shop  may  be  under  one  roof 
and  the  eye  bars  and  the  rivets  and  bolts  may  be  made  in  the  forge 
shop.  It  will  be  noted  that  similar  operations  are  carried  on  in  different 


departments,  but  this  is  a  matter  of  plant  economy.  For  instance, 
it  is  cheaper  to  maintain  milling  machines  and  boring  machines  in  the 
main  structural  shop  or  in  the  eye-bar  shop  as  well  as  in  the  machine 
shop  than  it  is  to  carry  all  of  the  heavy  members  to  the  machine  shop 
for  milling. 


PART  II  —  STRUCTURAL  DRAFTING 


CHAPTER  V 
STRUCTURAL  DRAWINGS  — THE  DRAWING 

SYNOPSIS:  In  the  first  chapters  of  this  Part  II  are  given  the  fundamental  principles 
of  drawing.  In  this  chapter  are  discussed  the  projection,  the  arrangement  and  the 
selection  of  views,  the  working  units,  and  the  scale. 


1.  A  Structural  Drawing  is  a  working  drawing  for  steel  construction, 
and  it  should  fully  represent  one  or  more  members  of  a  bridge,  a  building, 
or  other  similar  structure.     It  is  made  primarily  for  use  in  the  templet 
shop  and  the  structural  shop,  and  it  should  not  only  give  all  the  informa- 
tion necessary  for  the  construction  of  the  members  in  the  shop,  but  also 
provide  for  their  proper  connection  to  other  members  in  the  field.     Each 
member  is  composed  either  of  a  single  piece  of  structural  steel  or  a  com- 
bination of  the  common  rolled  steel  shapes,  and  for  this  reason  many 
methods  are  necessarily  used  which  are  peculiar  to  this  form  of  drawing  — 
methods  that  are  somewhat  different  from  those  used  in  other  kinds  of 
working  drawings.     It  is  essential  that  structural  drawings  be  made  and 
checked  carefully,  for  the  cost  of  replacing  ruined  pieces  is  great,  and  the 
resulting  delay  is  expensive. 

2.  A  structural  drawing  may  be  subdivided  into  the  following  ele- 
ments, which  will  be  discussed  in  separate  chapters: 

The  Drawing 

The  Conventional  Methods  of  Representation 

The  Conventional  Methods  of  Billing 

The  Dimensions 

The  Notes,  the  Title,  and  the  Border. 


THE  DRAWING 

3.  Projection.  —  Working  drawings  are  drawn  in  orthographic  pro- 
jection, and  the  third  angle  of  projection  is  used.     At  times  a  knowledge 
of  isometric,  oblique,  and  cabinet  projections,  and  of  perspective  drawing 
is  of  benefit  to  the  draftsman,  although  usually  not  essential.     In  ortho- 
graphic projection,  a  "view  "  is  not  a  true  view  as  in  perspective  drawing, 
but  it  represents  the  projection,  by  parallel  lines,  of  one  face  and  the  pro- 
jecting parts  of  a  member  upon  either  a  horizontal  or  a  vertical  plane. 
A  view  which  is  projected  upon  a  horizontal  plane  is  termed  a  plan,  while 
a  view  projected  upon  a  vertical  plane  is  termed  an  elevation.     These 
terms  are  commonly  used  in  erection  diagrams,  "show  drawings,"  and 
design  sheets,  where  the  structure  is  treated  as  a  whole,  but  they  are  not 
often  applied  to  working  drawings  in  which  individual  members  are 
considered. 

4.  The  proper  views  of  any  member  should  be  selected  to  represent 
that  member  to  the  best  advantage.     Two  or  more  views  are  usually 
necessary,  but  no  more  views  should  be  drawn  than  those  required  to 
show  clearly  the  arrangement  of  the  different  pieces  of  which  the  member 
is  composed,  together  with  all  the  necessary  dimensions.    .Much  time 
and  space  may  be  wasted  by  drawing  unnecessary  views.     The  usual 


34 


PART   II  —  STRUCTURAL  DRAFTING 


— J 


TOP  VIEW 


SECTION 
AA 


[ 

END 
VIEW 


r 

j 

1  (FRONT  \ 

\    \     VIEW     , 

1        1 

i  1 

SECTION                ^A 

END 
VIEW 


BOTTOM  SECTION 


Fig.  34.    Arrangement  of  Views. 


views  employed  are:  —  the  front  view  or  front  elevation,  the  top  view, 
the  bottom  section,  and  the  end  views.  A  rear  view  becomes  necessary 
in  some  cases,  and  frequently  one  or  more  sectional  views. 

1.  All  views  must  bear  a  proper  relation  to  one  another  as  in  Mechani- 
cal Drawing;  see  Fig.  34.     The  top  view  must  be  placed  directly  above 
the  front  view,  and  an  end  view  opposite  the  front  view  near  the  end  it 

represents.  It  is  cus- 
tomary in  making  struc- 
tural drawings  to  replace 
the  bottom  view  by  a 
bottom  sectional  view 
placed  directly  below  the 
front  view,  but  drawn  as 
seen  from  above.  The 
section  plane  is  assumed 
to  be  passed  just  above  the  bottom  details  which  are  to  be  shown,  in  such 
a  manner  that  comparatively  few  parts  are  cut.  .See  page  37  :  2. 

The  reason  for  substituting  a  bottom  section  for  a  bottom  view  is  to  obtain  a  better 
correlation  between  it  and  the  top  view,  so  that  it  will  be  more  apparent  whether  a 
connection  on  one  side  of  the  top  flange  and  a  connection  on  the  bottom  flange  are  on 
the  same  or  the  opposite  sides  of  the  member.  , 

A  sectional  view,  other  than  the  bottom  section,  may  be  placed  any- 
where on  the  sheet,  provided  the  position  of  the  section  is  clearly  indi- 
cated. It  is  the  usual  practice,  however,  to  place  the  sectional  view 
either  at  the  end  of  the  member,  adjacent  to  or  in  place  of  an  end  view, 
or  else  in  a  break  in  the  member,  preferably  in  the  main  or  front  view  at 
the  point  where  the  section  is  taken.  In  any  case  the  sectional  view  must 
be  drawn  as  seen  looking  toward  the  parts  which  are  to  be  shown. 

2.  The  distances  between  the  different  views  of  a  member  are  not 
necessarily  equal,  but  they  are  made  just  great  enough  to  provide  ample 
room  for  dimension  lines,  explanatory  notes,  and  other  lettering  which 
must  be  put  on  the  sheet.     Provision  should  be  made  also  for  any  pro- 
jecting parts,  such  as  gusset  plates,  base  plates,  or  connection  angles. 

3.  The  Position  on  the  Sheet.  —  Most  members  are  shown  on  the 
drawing  separately,  but  in  some  classes  of  work,  as  for  example  truss 
work,  it  is  convenient  to  draw  several  members  together,  even  though 


they  are  to  be  shipped  separately,  in  order  to  show  their  relation  to  each 
other  and  to  save  the  duplication  of  details.  (See  Fig.  122.)  As  far  as 
practicable  it  is  well  to  draw  horizontal  members  horizontally  on  the 
sheet,  i.e.,  lengthwise,  and  to  draw  vertical  members  vertically,  i.e., 
from  the  lower  to  the  upper  edges  of  the  sheet.  Long  columns,  or  other 
vertical  members  which  would  appear  too  crowded  in  this  position  may 
be  drawn  lengthwise  of  the  sheet.  Inclined  members  may  be  drawn 
horizontally  in  order  to  economize  space,  unless  it  is  desired  to  show  their 
relation  to  other  members.  It  is  desirable  to  draw  each  member  in  such 
a  position  that  the  plans  and  the  diagrams  can  be  used  to  the  best  ad- 
vantage, without  turning  them  needlessly. 

4.  Parts  Shown.  —  Only  the  pieces  which  are  to  be  shipped  with  a 
member  should  be  shown  on  the  detail  drawing  of  that  member,  although 
in  unusual  or  complicated  work  part  of  a  connecting  member  may  be 
shown  in  outline,  by  the  use  of  dotted  lines  or  lines  of   red  ink  (page 
36  :  2).     This  should  be  done  for  the  benefit  of  other  draftsmen  or  of 
the  erector,  only  to  make  more  clear  a  connection  which  might  otherwise 
be  obscure  or  difficult  to  understand  from  the  drawing  —  never  if  con- 
fusion is  likely  to  result  in  the  shop.     In  drawing  any  view  of  a  member 
it  is  unnecessary  to  show  all  the  parts,  such  as  connection  angles  or  plates 
or  rivet  heads,  which  project  from  faces  other  than  the  principal   one 
shown,  merely  for  the  sake  of  completeness;  as  a  rule  the  drawing  is 
thereby  complicated,  and  valuable  time  is  wasted.     They  should  be 
shown,  however,  if  the  drawing  is  made  more  clear,  or  if  an  extra  view 
may  be  dispensed  with  by  so  doing. 

5.  If  a  member  is  practically  symmetrical  about  its  center  line,  it  is 
necessary  to  show  only  one-half  of  the  member  with  a  note  to  the  effect 
that  it  is  "Symmetrical  about  the  center  line,"  or  "Symmetrical  about 
the  center  line  except  as  shown  or  noted,"  or  that  "The  other  half  is 
exactly  like  the  half  shown."      It  is  customary  to  show  the  left  end 
of  the   member.      See  page  86  :  5.     By  this  method   much   excessive 
duplication   may    be  avoided.      Simple    members    are    usually    shown 
completely.  i 

6.  The  usual  working  units  in  structural  work  are  feet  and  inches  and 
fractions  of  inches  expressed  to  the  nearest  sixteenth.     Since  many  of  the 
tapes  used  in  the  shop  are  subdivided  to  eighths  only,  it  is  more  con- 


CHAPTER   V 


STRUCTURAL  DRAWINGS  — THE  DRAWING 


35 


venient  for  all  concerned  to  use  multiples  of  |",  or  preferably  -J-",  when- 
ever practicable,  it  being  understood  that  each  dimension  is  correct  to 
within  sV'j  i.e.,  expressed  to  the  nearest  16th.  In  a  few  instances  it  may 
become  necessary  to  employ  dimensions  in  32nds,  where  dimensions  are 
subdivided,  or  in  64ths,  or  in  lOOths,  for  the  sizes  of  pin  holes. 

1.  In  order  to  obtain  the  best  arrangement  and  appearance  of  a  draw- 
ing, a  preliminary  freehand  sketch  of  each  member  should  be  drawn  on 
a  separate  sheet.     This  sketch  should  show  the  number  and  the  arrange- 
ment of  the  views,  the  main  dimensions,  the  number  of  dimension  lines, 
and  the  position  of  the  principal  connections.     The  sketch  need  not  be 
elaborate,  but  it  should  enable  the  draftsman  to  choose  the  best  scale,  to 
determine  the  distance  between  the  different  views,  to  plan  the  types  of 
connections  to  use,  and  to  report  any  missing  information  so  that  it  may 
be  supplied  with  the  least  possible  delay.     It  will  usually  be  found  that 
the  preparation  of  this  sketch  will  actually  save  more  time  than  is  con- 
sumed in  its  preparation,  and  in  addition  the  work  will  be  arranged  more 
advantageously. 

2.  Although  structural  drawings  are  for  the  most  part  drawn  approxi- 
mately to  scale,  it  is  unnecessary  and  undesirable  to  employ  the  same 
degree  of  accuracy  used  in  map  work;  one  is  never  permitted  to  scale  a 
drawing  to  obtain  a  dimension,  but  is  required  to  use  the  figured  dimen- 
sions only.     Time  should  not  be  wasted,   therefore,   in  too  accurate 
plotting,  but  greater  stress  should  be  laid  upon  giving  the  dimensions 
correctly.     The  more  complicated  drawings  are  drawn  to  a  definite  scale 
to  avoid  crowding,  and  to  simplify  the  addition  of  other  connections.     In 
simple  drawings,  however,  only  the  details  are  scaled,  and  the  lengths 
between  details  are  shortened  to  save  space.     Beams  are  usually  drawn 
upon  printed  forms  which  determine  the  outline  regardless  of  the  actual 
dimensions  required    (page   83  :  4).     The    details    may  be    drawn   to 
approximately  the  same  scale  as  the  depth  of  the  beam,  and  the  distances 
between    details    estimated    roughly    proportional   to   the    length.     In 
columns  or  other  long  members  it  is  sometimes  convenient  to  use  one 
scale  for  the  details  and  a  smaller  scale  for  the  distances  between  details, 
although  these  distances  may  frequently  be  estimated.     Small  distances, 
such  as  the  thicknesses  of  angles  or  plates,  are  often  exaggerated  on  small 
scale  drawings  to  prevent  the  lines  from  running  together.     After  a  little 


experience  the  draftsman  will  be  able  to  estimate  small  unimportant 
distances  without  the  scale. 

3.  The  Scale.  —  Structural  draftsmen  use  Architects'  scales  for  the 
most  part,  although  they  have  more  or  less  use  for  Engineers'  (decimal) 
scales  also.     The  adoption  of  the  best  scale  for  the  drawing  of  a  large 
member  depends  upon  the  size  of  the  piece,  the  size  of  the  sheet,  the 
number  of  the  views,  and  the  number  of  the  dimension  lines  required. 
In  some  cases  it  becomes  necessary  to  use  more  than  one  sheet  to  show  a 
member  properly.     It  is  seldom  practical  to  use  less  than  f  "  =  1'  except 
for  plans  and  diagrams.     The  scale  most  used  is  f"  =  1',  but  on  small  or 
complicated  drawings  the  draftsmen  often  prefer  to  use  1"  =  1'.     The 
scales  \\"  =  1'  and  3"  =  1'  are  used  only  for  enlarged  details  or  layouts. 

Either  flat  or  triangular  scales  of  different  lengths  and  with  different  graduations 
may  be  obtained.  Scales  one  foot  long  are  most  used.  Triangular  ones  have  all  the 
required  scales  on  one  piece,  but  some  draftsmen  prefer  several  flat  scales  instead. 
A  scale  guard  should  be  used  with  a  triangular  scale  to  prevent  mixing  different  scales 
on  one  drawing. 

The  scales  are  graduated  in  such  a  manner  that  dimensions  may  be  plotted  directly 
without  conversion.  The  main  numbered  divisions  of  any  of  the  scales  represent  feet, 
and  the  end  foot  is  subdivided  into  inches  and  fractions  of  inches.  Note  that  the  zero 
mark  for  both  the  feet  and  the  inches  is  at  the  end  of  this  first  foot  instead  of  at  the  end 
of  the  scale.  Dimensions  less  than  one  foot  may  be  plotted  to  a  given  scale  by  means 
of  the  graduated  end  foot  much  as  they  would  be  laid  off  full  size  with  an  ordinary 
foot-rule.  Dimensions  over  one  foot  may  be  plotted  at  one  setting  of  the  scale,  pro- 
vided the  scale  is  long  enough,  by  placing  the  proper  foot-mark  at  a  given  point  and 
by  plotting  the  other  point  opposite  the  proper  fraction  of  an  inch.  For  example,  to 
plot  4'-5J"  to  a  scale  of  f"  =  1'  select  the  proper  edge  of  the  scale  graduated  to 
i"  =  1'  and  place  the  number  4  (4  ft.  from  the  zero  mark)  at  one  end  of  the  required 
distance  and  plot  the  other  end  5J  one-inch  divisions  beyond  the  zero  mark  (i.e.,  6J" 
from  the  end  of  the  scale).  Fractions  smaller  than  those  represented  by  the  smallest 
subdivisions  may  be  interpolated. 

4.  The  Size  of  the  Drawings.  —  Most  structural  companies  have 
adopted  sheets  of  standard  size  for  their  drawings,  and  with  few  ex- 
ceptions all  drawings  are  made  to  conform  to  these  sizes.     The  size  of 
sheet  most  used  for  principal  details  and  for  diagrams  is  24"  X  36". 
Beams,  castings,  forge  work,  bills,  and  miscellaneous  lists  are  made  on 
smaller  forms  which  vary  in  size  with  the  different  companies.     Some 
companies  have  one  or  more  intermediate  sizes.     For  student  use,  "  Nor- 


PART  II  —  STRUCTURAL  DRAFTING 


mal  "  drawing  paper  (15"  X  22")  is  well  adapted  to  most  work,  the 
sheets  of  separate-leaf  note  books  being  used  for  smaller  drawings,  and 
"Double  Elephant"  (27"  X  40"),  or  one-half  of  "Double  Elephant" 
(cut  to  20"  X  27"),  for  larger  drawings.  For  beam  work  and  billing, 
small  "  Drafting  Forms  "  *  (8"  X  10|")  have  been  prepared  by  the 
author  to  correspond  to  similar  sheets  in  use  in  the  drafting  rooms  of 
structural  companies.  The  uses  of  these  forms  are  illustrated  in  Chap- 
ters XVII,  XXIV,  and  XXVII,  pages  83,  146,  and  167. 

1.  Drawings  are  made  either  on  paper  and  then  traced,  or  else  on 
tracing  cloth  directly.     The  beginner  should  draw  on  paper  first  and  then 
trace  his  work.     Many  experienced  draftsmen  make  complete  pencil 
drawings  and  then  have  them  traced  by  "tracers  "  whose  time  is  less 
valuable.     The  most  satisfactory  method  for  an  experienced  draftsman 
is  to  make  the  drawing  directly  on  the  cloth.     He  is  thus  enabled  to 
draw  many  of  the  lines  in  ink  without  preliminary  pencil  lines,  and  con- 
sequently much  time  is  saved.     Other  lines  may  be  penciled  on  the  cloth 
and  later  inked.     See  Chapter  XII,  page  65. 

2.  Black  waterproof  India  ink  is  used  for  structural  drawings  almost 
invariably.     Colored  inks  are  seldom  used.     Formerly  the  dimension 
lines  were  made  with  red  ink,  but  nearly  all  the  structural  companies 
have  changed  to  the  use  of  black,  because  the  red  lines  do  not  show  dis- 
tinctly on  the  blueprints.     Since  the  shopmen  work  from  prints  entirely, 
and  use  only  the  given  dimensions  without  scaling,  it  is  important  that 
the  dimension  lines  be  clearly  defined.     Red  ink  is  occasionally  adopted 
to  indicate  parts  of  other  members  which  are  to  connect  to  the  one  being 
drawn,  in  case  the  detail  is  complicated  or  unusual  (page  34  :  4).     The 
red  ink  is  easily  seen  on  the  tracings  by  the  draftsmen  who  are  chiefly 
interested  in  it,  and  the  lines  may  be  faintly  discerned  on  the  prints  by  the 
erector  without  causing  any  confusion  to  the  shopmen.    However,  red  ink 
can  be  erased  only  with  difficulty  and  some  red  inks  are  liable  to  spread  after 
the  drawings  are  filed  in  cold  vaults;  the  use  of  red  ink  should  be  limited. 

3.  The  best  results  in  drafting  may  be  obtained  by  adopting  some 
systematic  method  of  procedure.     This  not  only  saves  time,  but   also 
minimizes  the  chance  of  making  mistakes,  or  of  overlooking  connections. 
Each  draftsman  may  adopt  his  own  method,  and  different  classes  of 

*  Published  by  John  Wiley  and  Sons,  Inc.,  New  York. 


drawings  may  require  different  steps,  but  the  following  order  of  pro- 
cedure will  form  a  guide  to  the  student  when  making  a  pencil  drawing. 
Similar  suggestions  may  be  found  for  tracing  (page  59  :  9),  and  for 
drawing  directly  on  cloth  (page  66  :  4). 

1st.  Make  a  rough  sketch  of  the  member  on  a  separate  paper,  indicat- 
ing the  position  of  each  connection,  thus  determining  the  number 
of  views  and  the  number  of  dimension  lines.  It  is  well  to  deter- 
mine the  main  dimensions  also  before  starting  the  final  drawing. 

2nd.  Outline  the  principal  view  first,  and  draw  the  corresponding 
dimension  lines. 

3rd.  Outline  the  other  views  and  draw  the  dimension  lines.  If 
preferred,  the  principal  view  may  be  completed  first. 

4th.     Write  on  the  main  dimensions. 

5th.  Draw  the  details  in  the  order  of  importance,  beginning  with  the 
connections  to  the  supports,  if  any.  Put  on  each  dimension  as 
soon  as  determined,  indicate  the  rivets  and  the  holes,  bill  all  the 
material,  and  add  the  necessary  notes  before  proceeding  to  the 
next  connection. 

The  draftsman  should  constantly  imagine  himself  in  the  place  of  the  men 
in  the  shop  in  order  to  determine  what  information  is  needed  on  a  drawing 
and  how  this  information  can  be  arranged  to  be  of  the  greatest  service.  He 
should  improve  every  opportunity  to  watch  the  shopmen  at  work,  and  to 
become  familiar  with  their  methods.  He  should  attempt  to  build  up  the 
drawing  of  a  member  in  much  the  same  order  in  which  the  member  itself 
is  built  up  in  the  shop,  and  he  should  never  submit  a  drawing  to  be  checked 
until  he  is  satisfied  that  the  members  can  be  constructed  as  intended. 

6th.     Complete  the  dimensions  between  the  connections,  spacing 

necessary  rivets  or  lattice  bars. 
7th.     Note  the  sizes  of  the  rivets  and  the  .holes. 
8th.     Make  the  title,  and  add  any  general  notes  which  may  be  required. 

4.  A  draftsman  should  always  check  his  own  work  as  he  goes  along. 
He  should  thus  be  able  to  detect  any  blunders  in  time  to  correct  them 
before  a  large  amount  of  dependent  work  has  been  wasted.  He  can  often 
save  more  time  than  he  consumes  in  applying  his  checks,  and  in  addition 
he  is  able  to  submit  to  the  checker  drawings  which  are  comparatively 
free  from  mistakes  —  a  point  very  much  in  his  favor.  See  page  180  :  1. 


CHAPTER  VI 


STRUCTURAL  DRAWINGS  — THE   CONVENTIONAL  METHODS 
OF   REPRESENTATION 

SYNOPSIS:  In  Structural  Drawings  the  objects  are  not  always  represented  in  exact 
accordance  with  the  principles  of  orthographic  projection;  certain  lines  are  omitted 
for  the  sake  of  simplicity,  especially  those  which  represent  curved  surfaces.  Such 
omissions,  and  the  conventional  methods  of  representing  the  common  structural 
shapes,  are  explained  in  this  chapter. 


1.  The  lines  of  a  drawing  are  usually  made  of  two  widths;  see  Fig.  37. 
The  dimension  lines,  the  rivet  lines,  the  projection  lines,  the  working 
lines,  and  the  cross-section  lines  are  full  black  lines  made  as  fine  as  prac- 
ticable, but  not  so  fine 
as  to  appear  ragged  on 
the  tracing  or  on  the 
blueprint.  The  lines 
which  represent  the  com- 
ponent parts  of  the  mem- 
)  sect/on  pianes- /arge  ber  itself  are  black  lines 

mBardes  Lines 


Dimension  Lines,  etc. 

natal/  Lines  -  MUe 

Detail  Lines- invisible 

Center  Lines 


Section  Planes -t 


Fig.  37.   The  Lines  of  a  Drawing. 


made  heavy  enough  to 
show  a  contrast  with  the 
finer  lines  noted  above. 
The  lines  which  represent  visible  edges  are  made  full,  and  those  which 
represent  invisible  edges  are  made  dashed.  The  dashes  should  be 
about,  one-eighth  inch  long,  drawn  as  close  together  as  practical,  but 
with  sufficient  space  between  them  so  that  on  blueprints  the  lines  are 
clearly  dashed  lines  and  not  full  lines.  In  short  lines,  or  in  the  lines  of 
small-scale  drawings,  the  dashes  may  be  shorter,  and  conversely  may 
be  lengthened  in  very  long  lines,  particularly  in  drawings  which  are 
made  to  a  large  scale.  The  appearance  of  a  drawing  is  greatly  im- 
proved if  large  or  uneven  spaces  between  the  dashes  are  avoided. 


Where  lines  are  close  together,  the  dashed  lines  may  be  made  slightly 
narrower  than  the  full  lines.  Dashed  lines  are  liable  to  be  wider  than  full 
lines  unless  the  setting  of  the  pen  is  changed.  Center  lines  are  fine  black 
lines,  similar  to  dimension  lines  except  that  they  are  made  of  dots  and 
dashes  alternating.  Lines  which  indicate  where  sections  are  taken,  are 
made  of  dashes  with  two  dots  between.  These  may  be  made  either  fine 
or  coarse,  depending  upon  which  will  show  the  most  contrast  with  the 
surrounding  lines.  They  may  be  continuous,  or  portions  of  them  may 
be  omitted  to  avoid  confusion  with  other  lines.  Arrows  should  be  placed 
at  the  ends  of  these  lines  to  show  which  part  of  a  cut  member  is  represented 
in  the  corresponding  sectional  view.  These  lines  which  indicate  a  section 
should  be  lettered  to  correspond  to  the  sectional  view.  Where  space 
permits,  circles  may  be  placed  at  the  ends  of  the  lines  with  the  letters 
inscribed ;  otherwise  the  letters  may  be  placed  at  the  ends  of  the  arrows. 
See  Fig.  37.  For  the  use  of  lines  wider  than  the  main  lines  of  the  draw- 
ing, see  pages  37  :  2,  and  54  :  7.  For  the  method  of  inking  wide  lines 
see  page  59 :  3.  Dotted  lines  should  be  reserved  for  indicating  compli- 
cated connections  (page  34  :  4). 

2.  Sectional  views  (page  34:1)  are  usually  "cross  hatched"  or 
"section  lined  "  so  that  they  may  be  distinguished  from  other  views. 
Only  the  parts  which  are  cut  by  the  section  plane  (page  34  :  1)  should 
be  section  lined,  and  the  position  of  this  section  plane  should  be  selected 


37 


38 


PART   II  — STRUCTURAL   DRAFTING 


to  illustrate  the  conditions  to  the  best  advantage.  It  is  usually  best  to 
cut  only  continuous  material  so  that  the  details  will  stand  out  more 
clearly.  The  cross-section  lines  are  fine  black  lines  (see  above)  drawn  at 
uniform  distances  apart,  inclined  45°  with  the  principal  edges  of  the 
parts  cut.  It  is  preferable  to  slope  the  section  lines  of  adjacent  compo- 
nent parts  in  opposite  directions  in  order  to  accentuate  the  dividing  sur- 
faces. The  webs  of  I-beams  and  channels  which  are  cut  by  section  planes 
are  usually  made  solid  black  for  simplicity  instead  of  section  lined ; 
similarly  web  plates  are  sometimes  made  solid,  as  in  the  bottom  sectional 
views  of  plate  girders. 

There  are  many  devices  on  the  market  to  aid  the  draftsman  in  spacing  the  section 
lines  uniformly,  but  with  a  little  experience  one  can  produce  results  which  are  quite 
satisfactory  for  this  class  of  work  with  simply  a  T-square  and  a  triangle.  If  desired, 
the  advance  of  the  triangle  can  be  made  more  uniform  by  means  of  a  small  strip  of 
wood  cut  slightly  smaller  than  the  opening  in  the  triangle.  By  alternately  holding  and 
eliding  the  wood  and  the  triangle  the  latter  may  be  advanced  in  accordance  with  the 
amount  of  clearance  allowed. 

1.  Breaks.  —  When  part  of  a  view  is  omitted  the  broken  ends  should 
be  made  so  that  they  may  be  clearly  distinguished  from  the  actual  ends. 
An  irregular  freehand  line  may  be  drawn  to  represent  an  imaginary  cut 
across  the  member,  but  care  should  be  taken  not  to  draw  such  a  line 
across  a  space  between  component  parts  where  nothing  is  cut.  These 
irregular  lines  may  be  omitted  if  the  limits  of  each  view  stand  out  clearly 
from  the  dimension  lines  and  from  the  other  views.  When  a  member  is 
symmetrical  about  its  center  line  and  only  one  half  is  detailed,  the  main 
lines  of  the  drawing  should  not  be  stopped  abruptly  at  the  center  line 
but  should  be  extended  short  distances  beyond ;  in  this  way  one  can  tell 
at  a  glance  whether  one  half  or  the  whole  of  the  member  is  shown.  Typi- 
cal breaks  are  shown  in  Figs.  102,  122,  127,  and  143. 


Fig.  38  (a). 


Occasionally  it  may  be  desirable  to  indicate  the  true 
shape  of  a  simple  piece  at  the  break  in  order  to  dis- 
pense with  an  additional  view.  This  method  is  illustrated  by  Fig.  38  (a) ,  in 
which  the  piece  is  considered  to  be  cut  by  a  plane  at  45°.  This  method  is 
not  recommended  for  structural  drawings  although  it  is  sometimes  used. 
2.  Curved  surfaces  may  be  indicated  by  shade  lines  if  it  is  deemed 
advisable  in  order  to  illucidate  the  drawing  (Fig.  40  (d)),  but  usually  this  is 


unnecessary.  Some  of  the  surfaces  of  the  common  structural  shapes  are 
connected  by  "fillets"  with  curved  surfaces  (page  26  :  1),  but  it  is 
customary  to  omit  these  curves  from  most  drawings.  Should  it  become 
necessary  to  show  the  actual  forms,  the  dimensions  given  in  Fig.  25  (6)  may 
be  used. 

3.  For  the  most  part  a  conventional  representation  is  shown  for  each 
commercial  shape  of  structural  steel  whether  drawn  separately  or  in 
combination  with  other  shapes.     This  results  in  a  considerable  saving  of  . 
time  and  hence  of  money.     The  main  dimensions  are  usually  scaled,  but 
an  experienced  draftsman  may  estimate  the  spaces  between  some  of  the 
lines,  as,  for  example,  those  which  represent  the  thickness  of  metal.     As 
a  guide  to  the  student,  suggestions  are  here  given  to  enable  him  to  show 
each  shape  in  the  conventional  manner. 

4.  The  shapes  most  used  in  structural  work  are  plates,  angles,  I-beams, 
channels,  and  round  rods.     Less  frequently,  Tees,  Z-bars,  rails,  eye  bars, 
and  square  rods  are  used. 

5.  A  plate  is  indicated  in  any  view  by  a  rectangle  of  the  proper  dimen- 
sions.    The  width  and  the  length  are  scaled,  but  the  thickness  is  usually 
estimated;  the  thickness  is  often  exaggerated,  if  necessary,  to  show  clearly 
whether  a  dimension  extends  to  the  face  of  the  plate  or  to  the  center  line. 

6.  An  angle  is  shown  in  its  true  shape  in  the  end  view  (Fig.  38  (&))  ex- 
cept that  the  curves  are  omitted.     (Compare  Fig.  25  (6).)     The  front  and 
the  top  views  each  have  three  lines 

drawn  so  that  they  bear  the  proper  CH 

relation  to  the  lines  of  the  end  view 

in  accordance  with  the  usual  prin-    $*       lj— -^-•*irf-t«?-"ES 

ciples    of    orthographic    projection.  Fig  3g  (b)    An  ^^ 

Thus  the  inner  line  must  be  placed 

near  the  proper  outer  line  and  be  made  full  or  dashed  according  to  the 

position  of  the  outstanding  leg.     The  lengths  of  the  legs  are  usually 

scaled,  and  also  the  thicknesses  of  heavy  angles;  the  thickness  of  an 

ordinary  angle  may  be  estimated. 

7.  An  I-beam  is  shown  conventionally  (Fig.  39  (a))  as  follows: 

End  View.  —  The  depth  and  the  flange  width  are  plotted  to  scale,  the 
flanges  being  symmetrical  about  the  web.  The  thickness  of  the  web  is 
estimated  and  often  exaggerated  if  necessary  to  indicate  clearly  whether 


Full  because    visible 


CHAPTER  VI 


THE   CONVENTIONAL  METHODS  OF  REPRESENTATION 


39 


a  dimension  extends  to  the  face  of  the  web  or  to  the  center  line.  The 
outside  edges  of  each  flange  are  made  approximately  of  the  same  thick- 
ness as  the  web,  and  from  the 
points  thus  located,  sloping  lines 
are  drawn  until  they  intersect  the 
web  lines;  all  curves  are  omitted. 
(Compare  Fig.  25  (6) .)  These  lines 
are  drawn  to  a  slope  of  2  in  12. 


To Sqele 


.Dashed  because  Invisibly 

Appro  A  Imately  /?  f 


Thickness  "t"  estimated 


Solid  because  cut  by  section  plane 


Fig.  39  (a).   An  I-beam. 


Fig.  39(6). 


The  lines  which  represent  the  inner 
surfaces  of  the  flanges  of  all  standard 
I-beams  and  channels  have  a  slope  of  2  in  12.  These  lines  may  be  drawn  most  con- 
veniently and  uniformly  by  means  of  a  "beam  bevel,"  which  may  be  bought  or  easily 
made  of  celluloid,  wood,  or  cardboard,  in  a  form  similar 
to  that  shown  in  Fig.  39  (6).  For  occasional  use  a  beam 
bevel  may  be  added  to  a  celluloid  triangle  either  by 
cutting  the  bevels  on  the  edge  of  the  central  opening,  or  by 
scratching  one  or  two  sloping  lines,  as  shown  in  Fig.  39  (c) . 
One  of  these  lines  may  be  placed  coincident  with  the 
flange  line  (perpendicular  to  the  web)  and  then  the  whole 
triangle  may  be  moved  parallel  to  itself  until  the  edge  gives  the  desired  slope  line. 

Front  View.  —  Each  flange  of  the  I-beam  is  represented  conventionally 
by  two  full  lines  spaced  approximately  to  show  the  mean  flange  thickness. 
The  distance  between  the  outer  lines  of  the  two 
flanges  is  the  depth  of  the  beam  to  scale;  each 
inner  line  is  drawn  so  that,  if  extended,  it  would 
cut  the  sloping  lines  of  the  end  view  about  mid- 
way between  the  web  and  the  edges  of  the  flange. 
The  distance  between  the  two  lines  of  each  flange 
is  roughly  one  and  one-half  times  the  web 
thickness. 

Top   View.  —  Two  full  lines  are  drawn  to  show 
the   flange  width  to  scale.      The  web  is  shown 


Fig.  39  (c). 


midway  between  these  lines  by  two  dashed   (invisible)  lines,  the  web 
thickness  being  estimated  as  before. 

Bottom  Section.  —  This  is  similar  to  the  top  view  except  that  the 
web  is  shown  by  a  heavy  black  line  equal  in  width  to  the  web  thickness 
(page  37:  2). 


fDssheti 

because  invisible 

? 

Sea,, 

'*-—*-      " 

^Approximately 

£ 

ife 

•S.S 

E 

1 

Thickne 

is  "t"  estimated 

1.  A  channel  is  shown  conventionally  (Fig.  39  (d))  as  follows: 

End  View.  —  The  depth  and  the  flange  width  are  plotted  to  scale. 
The  thickness  of  the  web  is  estimated  and  often  exaggerated  if  necessary 
to  indicate  clearly  whether  a  dimension  extends -to  the  back  of  the  web 
or  to  the  center  line.  The  edge  of  each  flange  is  made  approximately  of 
the  same  thickness  as  the  web,  and  from  the  point  thus  located  a  sloping 
line  is  drawn  until  it  intersects  the  inner  web  line;  all  curves  are  omitted. 
(Compare  Fig.  25  (6).)  This  line  is  drawn  to  a  slope  of  2  in  12.  (See 
note  in  fine  print  under  I-beam.) 

Front  View.  —  Each  flange  of  the  channel  is  represented  conventionally 
by  two  lines  spaced  approximately  to  show  the  mean  flange  thickness. 
The  distance  between  the  outer 
lines  of  the  two  flanges  is  the 
depth  of  the  channel  to  scale; 
each  inner  line  is  drawn  so  that, 
if  extended,  it  would  cut  the 
sloping  line  of  the  end  view 
about  midway  between  the  web 
and  the  edge  of  the  flange.  The 
distance  between  the  two  lines  of  each  flange  is  roughly  one  and  one-half 
times  the  web  thickness.  The  inner  lines  of  the  flanges  are  full  or 
dashed,  depending  upon  whether  the  flanges  are  on  the  near  side  or  on 
the  far  side  of  the  web;  this  should  correspond  to  the  way  the  flanges 
are  shown  in  the  end  view. 

Top  View.  —  Two  full  lines  are  drawn  to  show  the  flange  width  to 
scale,  one  line  showing  also  one  face  of  the  web;  a  single  dashed  line  is 
added  to  show -the  other  face  of  the  web,  the  web  thickness  being  esti- 
mated as  before.  It  is  important  that  the  web  be  shown  on  the  proper 
side  of  the  flange  to  correspond  to  the  other  views. 

Bottom  Section.  —  This  is  similar  to  the  top  view  except  that  the 
web  is  shown  by  a  heavy  line  equal  in  width  to  the  web  thickness 
(page  37:2).  The  web  should  appear  on  the  same  side  as  in  the  top 
view. 

2.  Round  and  square  rods  are  represented  by  true  views,  the  ends 
being  shown  as  circles  or  squares,  and  the  other  views  as  rectangles.     No 
shade  lines  are  necessary. 


$o!id  because  cut  by  section  plane 


Fig.  39  (d).   A  channel. 


40 


PART  II  —  STRUCTURAL  DRAFTING 


-ft///  because    visible 


Fig.  40  (a).   A  Tee. 


1.    A  Tee  or  T-iron  is  shown  much  like  an  angle,  except  that  the  stem 
is  in  the  middle  of  the  flange,  and  hence  an  additional  line  is  required 

(Fig.  40  (a)).     Note  that  both  the 
— -    stem  and  the  flange  taper  slightly, 
but  in  most  drawings  they  may  be 
^3    represented  by  parallel  lines. 

2.   A  Z-bar  is  shown  convention- 
ally (Fig.  40  (6))  as  follows: 
End  View.  —  The  depth  and  the  flange  width  are  scaled,  but  the 
thickness  is  estimated  and  often  exaggerated ;  the  thickness  of  the  flanges 
is  uniform  and  is  equal  to  the  web  thickness. 

Front  View.  —  The  depth  is  shown  to  scale  between  two  full  lines. 
Additional  lines  are  drawn  just  inside  of  these  lines  to  represent  the  inner 
edges  of  the  flanges.  One  of  these 
lines  is  full  and  the  other  dashed, 
because  one  flange  is  on  the  near 
side  and  the  other  is  on  the  far  side  -g 
of  the  web;  this  should  correspond 
to  the  way  the  flanges  are  shown  in 
the  end  view. 


E 


/Daahed  because  invisible 


^~Full  because    -visible 
/Dashed  because  invietble 


**  Vu/y  because    visible 

Fig.  40  (6).  A  Z-bar. 


Top  View.  —  The  top  flange  is  shown  to  scale  between  two  full  lines, 
one  line  showing  also  one  face  of  the  web ;  a  dashed  line  is  added  to  show 
the  other  face  of  the  web,  the  web  thickness  being  estimated  as  before. 
A  fourth  line  is  drawn  to  show  the  outer  edge  of  the  bottom  flange,  the 
space  between  it  and  the  dashed  line  representing  the  flange  width  to 

scale.     The  position  of  the  full  and 
the  dashed  web  lines  should  corre- 
i    spond  to  the  other  views. 

JL       I  1        3.   A  rail  is  shown  conventionally 

Fig.  40  (c).  A  Rail.  (Fig-  40  (c))  as  follows: 

End  View.  —  The  head,  the  web, 

and  the  flange  are  drawn  from  the  dimensions  given  on  page  317.  On 
large  scale  drawings  these  are  drawn  to  scale,  and  the  curves  are  often 
shown.  Ordinarily,  however,  straight  lines  are  sufficient,  the  depth,  the 
width  and  the  thickness  of  the  head,  and  the  width  of  the  flange  being 
scaled. 


Front  View.  —  The  head  and  the  flange  of  the  rail  are  each  shown  con- 
ventionally by  two  lines  spaced  approximately  to  show  the  mean  thick- 
ness. The  distance  between  the  upper  line  of  the  head  and  the  lower 
line  of  the  flange  is  the  depth  of  the  rail  to  scale;  each  inner  line  is  drawn 
so  that,  if  extended,  it  would  cut  the  sloping  lines  of  the  end  view  about 
midway  between  the  web  and  the  outer  edges  of  the  head  or  of  the 
flange. 

Top  View.  —  The  widths  of  the  head  and  of  the  flange  are  each  shown 
by  two  lines  to  scale.  These  lines  are  placed  symmetrically  about 
two  dashed  lines  which  represent  the  web,  the  web  thickness  being 
estimated. 

4.  An  eye  bar  is  shown  in  the  main  view  to  scale,  from  the  dimensions 
given  in  the  handbooks  of  the  steel  companies.     The  actual  curves  are 
drawn  to  scale.     The  edge  and  the  end  views  appear  as  simple  rectangles, 
although  the  curves  are  sometimes  indicated 

by  line  shading,  as  shown  in  Fig.  40  (d). 

5.  Lattice    bars    are    usually    made    from 

standard  dies  according  to  the  billed  size,  as    E=3IB!nio==^==^=^=, 
explained  on  page  45  :2.     For  this  reason  it  is      Fig.  40  (d).  An  Eye  Bar. 
unnecessary  to  show  the  bars  on  a  drawing  in 

detail.  One  or  two  bars  are  often  shown  on  each  sheet,  being  drawn 
from  the  dimensions  given  on  page  315;  other  bars  are  indicated  simply 
by  center  lines  drawn  from  center  to  center  of  end  rivets,  as  shown  in 
Fig.  137.  Often  the  intermediate  bars  and  rivets  of  a  group  may  be 
omitted  (compare  page  41  :  1),  only  one  or  two  bars  being  shown  or 
indicated  at  each  end  of  the  group.  Dashed  lines  instead  of  full  lines 
are  sometimes  used  to  indicate  an  independent  system  of  lattice  bars,  as 
for  example,  when  the  bars  on  opposite  sides  of  a  member  are  shown  in 
one  view  (Fig.  129). 

6.  Shop  rivets  and  holes  for  field  rivets  are  usually  indicated  in  the 
views  where  they  appear  as  circles  according  to  the  Osborne  Code,  as 
shown  on  page  304.     An  open  circle  of  the  diameter  of  the  rivet  head 
indicates  the  shop  rivet,  and  a  circle  of  the  diameter  of  the  rivet  hole,  but 
inked  solidly,  represents  the  field  rivet.     The  diameter  of  the  rivet  hole 
is  V/'  greater  than  the  diameter  of  the  shank  of  the  rivet  (page  30  :  4), 
while  the  diameter  of  the  head  is  as  given  on  page  304.     The  draft 


'  drafts- 


CHAPTER  VI 


THE   CONVENTIONAL   METHODS   OF   REPRESENTATION 


41 


man  can  usually  estimate  the  sizes  of  the  circles  closely  enough  when 
drawing  to  an  ordinary  scale;  but  he  should  be  particular  to  show  a  con- 
trast in  size  between  the  shop  and  the  field  rivets  as  an  added  safeguard 
in  case  he  should  neglect  to  fill  in  all  the  field  rivets.  It  is  well  to  re- 
member that  for  a  rivet  of  a  given  size  the  diameter  of  the  circle  for  a 
shop  rivet  is  approximately  one  and  one-half  times  as  large  as  the  diam- 
eter of  the  circle  for  a  field  rivet. 

After  making  a  sample  circle  preparatory  to  drawing  a  large  number  of  rivets,  the 
beginner  should  measure  the  diameter  to  see  if  it  is  approximately  to  scale;  in  fact, 
this  test  is  so  quickly  made  that  an  experienced  draftsman  can  often  apply  it  to 
advantage,  particularly  when  drawing  to  a  small  scale. 

Other  views  of  rivets  and  holes  are  shown  only  when  an  extra  view  may 
be  avoided  or  the  drawing  may  be  made  more  clear  thereby.  In  general 
the  side  or  the  sectional  view  of  a  hole  for  a  field  rivet  is  a  rectangle  filled 
in  solid.  A  similar  open  rectangle  represents  the  shank  of  a  shop  rivet 
to  which  are  added  semi-circular  heads.  See  G20,  Fig.  92.  When 
shop  rivets  are  countersunk,  cross  lines  are  drawn  perpendicularly  to  each 
other  and  preferably  at  45°  with  the  rivet  lines.  See  page  304.  If 
countersunk  on  the  near  side  (outside)  the  lines  are  only  outside  the  circle, 
and  if  countersunk  on  the  far  side  (inside) ,  the  lines  are  inside.  Similarly 
the  lines  extend  outside  and  inside  if  countersunk  on  both  sides.  To 
show  this  distinction  in  field  rivets,  auxiliary  circles  must  be  placed  out- 
side the  others.  Flattened  rivets  are  indicated  by  lines  which  slope  in 
one  direction  only,  preferably  at  45°  with  the  rivet  lines.  The  number 
of  sloping  lines  shows  the  height  of  the  rivet  head  in  eighths  of  an  inch, 
i.e.,  three  lines  for  f "  and  two  lines  for  \".  Rivets  flattened  to  |"  would 
be  useless  but  they  may  be  countersunk  without  being  chipped  after  they 
are  driven;  they  will  then  not  project  more  than  one-eighth  inch.  In 
order  to  insure  the  detection  of  countersunk  or  flattened  rivets,  notes  are 
often  added  to  supplement  the  code,  especially  when  the  rivets  are  in  un- 
usual places,  as  for  example:  "Rivets  countersunk  far  side  but  not 
chipped,"  "Rivets  countersunk  and  chipped  both  sides,"  or  "Rivets 
flattened  to  \"  near  side."  (Figs.  129  and  133.)  Such  notes  are  omit- 
ted on  shoe  plates  and  column  bases,  or  wherever  rivets  are  usually 
countersunk,  provided  they  are  clearly  indicated.  Rivets  should 


never  be  countersunk  in  metal  thinner  than  that  indicated  in  the  table 
on  page  304. 

1.  All  holes  for  field  rivets  are  usually  shown,  except  in  plate  work  or 
other  work  which  requires  a  large  number  of  field  rivets,  the  position  of 
which  can  be  clearly  indicated.     All  shop  rivets  should  be  shown  in 
small  connections  and  in  all  doubtful  places,  but  some  may  be  omitted 
when  in  large  numbers  if  no  ambiguity  is  likely  to  result.     A  short  line 
crossing  the  rivet  line  is  often  used  to  indicate  the  center  of  a  rivet.     When 
shop  rivets  are  dimensioned  in  a  group  (page  49  :  7),  the  rivets  at  the 
ends  of  the  group  are  shown,  but  most  of  the  intermediate  ones  may  be 
omitted ;  it  is  well  to  indicate  one  space  at  each  end  of  the  group  by  means 
of  a  rivet  or  a  cross  line  in  order  to  emphasize  the  presence  of  intermediate 
rivets.     On  the  pencil  drawing  enough  rivets  and  holes  should  be  shown 
to  distinguish  clearly  between  them  when  the  tracing  is  made,  without 
the  necessity  of  further  investigation.     They  may  be  made  freehand  in 
pencil,  but  they  should  be  carefully  made  with  a  bow-pen  or  a  "riveter  " 
(page  69  :  3)  on  the  finished  drawing. 

2.  Bolts  are  occasionally  drawn  to  scale  from  the  actual  dimensions 
(page  304),  but  ordinarily  simply  the  holes  for  the  bolts  are  indicated 
in  the  same  way  as  holes  for  field  rivets,  whether  the  bolts  are  to  be  in- 
serted in  the  shop  or  in  the  field.     Shop  rivets  should  never  be  shown 
where  bolts  are  to  be  used.     Bolts  which  are  put  in  place  permanently 
in  the  shop  should  be  billed  and  noted  on  the  drawing  (page  53  : 3).     If 
necessary  to  differentiate  between  shop  and  field  bolts,  small  squares  may 
be  drawn  around  the  solid  circles  for  the  shop  bolts  as  illustrated  in  Fig. 
140, 

3.  Fillers  are  used  to  fill  the  spaces  between  other  surfaces  and  it  is 
not  usually  necessary  to  draw  any  additional  lines  to  represent  them, 
since  the  lines  would  be  coincident  with  lines  already  drawn.     When 
clearance  is  allowed  between  the  edges  of  the  fillers  and  adjacent  edges, 
additional  lines  (dashed  if  invisible)  may  be  drawn,  although  these  are 

.sometimes  omitted  if  the  drawing  is  clearer  without  them.  Round 
washers  are  used  as  fillers  where  there  is  only  a  single  rivet,  as  at  stitch 
rivets  (page  69  :  4). 

4.  Bent  Plates.  —  The  true  projections  of  bent  plates  and  angles  are 
usually  simplified  as  shown  in  Figs.  143  and  149.     The  dimensions  must 


42 


PART   II  —  STRUCTURAL   DRAFTING 


be  shown  accurately  in  the  proper  views,  but  most  drawings  would  be 
complicated  unnecessarily  by  an  attempt  to  show  all  the  edges.  Often 
the  drawing  may  be  clearer  and  more  easily  interpreted  if  one  view  is 
drawn  as  if  the  plate  or  angle  were  not  bent.  The  rivets  and  holes  in 
inclined  surfaces  would  appear  as  ellipses  instead  of  circles  (Fig.  78), 
but  on  account  of  the  difficulty  in  making  small  ellipses  this  distinction 


is  not  always  made  on  the  drawing  unless  ambiguity  would  result  from  the 
use  of  circles. 

1.  Other  Materials.  —  It  is  sometimes  convenient  to  represent  ma- 
terials other  than  steel  according  to  standard  conventions.  The  more 
common  conventions  for  this  class  of  work  are  shown  in  Fig.  42. 


CORRUGATED  STEEL 


WOOD 


GLASS 


Fig.  42.   Conventional  Representations. 


CHAPTER  VII 


STRUCTURAL  DRAWINGS  — THE   CONVENTIONAL  METHODS 

OF  BILLING 

SYNOPSIS:  In  Structural  Drafting  the  term  "billing"  has  two  meanings,  viz.:  (1) 
the  statement  on  a  drawing  of  the  number  and  the  size  of  the  component  parts  of  a 
member;  and  (2)  the  preparation  of  a  list  or  "bill"  which  is  a  summary  of  all  the 
material  used  in  the  construction  of  one  or  more  members,  as  an  order  bill  (page  162  : 1), 
or  a  shop  bill  (page  167  :  1).  In  this  chapter  are  explained  the  conventional  methods 
of  billing  material  on  the  drawings. 


1.  Billing.  —  The  size  or  description  of  each  component  part  of  any 
member  should  be  expressed  or  "billed  "  on  the  drawing  near  the  prin- 
cipal view  of  that  part.  When  two  or  more  identical  pieces  occur 
together  they  may  be  billed  together,  but  the  number  of  pieces  should 
indicate  the  number  required  at  only  one  point  of  a  single  member. 
The  object  of  billing  is  to  show  the  commercial  shape  from  which  the 
part  is  to  be  cut,  and  the  length  of  such  shape  required.  The  methods 
of  billing  must  conform  to  the  usual  practice  and  indicate -the  com- 
mercial shapes  in  the  same  way  that  they  are  listed  in  the  handbooks 
of  the  steel  companies.  The  bill  of  material  serves  as  the  "name  "  of 
a  piece,  not  only  upon  the  drawing,  the  order  bill,  and  the  shop  bill,  but 
also  upon  the  steel  itself;  it  is  painted  upon  the  steel  at  the  rolling  mill 
as  soon  as  the  steel  is  cut  to  the  ordered  length,  and  it  is  used  for  iden- 
tification until  the  piece  is  placed  in  its  final  position  in  the  structure, 
or  until  it  is  assembled  with  other  pieces  to  form  a  member  which  is 
subsequently  identified  by  means  of  a  shipping  mark  (page  80  :  6). 

At  the  mill,  the  contract  number  as  well  as  the  bill  of  material  is  painted  on  the 
steel.  If  the  material  is  recut  in  the  shop  to  shorter  lengths,  the  contract  number  and 
the  revised  bill  are  painted  on  each  piece,  along  with  the  shipping  mark  and  the  assem- 
bling mark,  if  any  (page  79  :  2).  Similarly,  the  templets  are  marked  to  correspond. 
After  a  member  is  assembled  and  riveted  it  is  painted  before  it  is  shipped;  the  con- 


tract number  and  the  shipping  mark  are  left  uncovered  or  are  repainted  for  use  during 
shipment  and  erection. 

2.  Certain  abbreviations  and  conventional  signs  are  used  in  billing, 
as  shown  in  the  following  paragraphs.  The  multiplication  sign  (x)  is 
used  simply  to  distinguish  the  different  dimensions.  It  is  pronounced 
"by";  thus  8  X  \  X  12'-0"  is  read  "eight  by  one-half  by  twelve  feet, 
no  inches."  Similarly,  the  sign  (#)  is  used  for  "pounds,"  (#/ft.)  for 
"pounds  per  foot"  and  (#/yd.)  for  "pounds  per  yard."  In  billing, 
the  "per  foot"  and  often  the  "per  yard"  are  omitted.  The  size  of 
the  cross  section  is  expressed  in  inches  in  billing,  even  if  over  one  foot. 
The  length  is  the  extreme  distance  at  right  angles  to  the  other  figures; 
a  length  of  I'-O"  or  over  is  expressed  in  feet  and  inches,  while  a  length 
less  than  one  foot  may  be  written  in  inches  alone,  unless  it  seems  clearer 
to  prefix  the  0'  thus:  O'-IO".  See  the  illustrations  below.  The  con- 
ventional methods  of  billing  the  common  structural  shapes  are  as 
follows:  — 


3.   Plates: 

Number: 

(pieces) 

Thus:  1  PI.  8  X  \  X  10",  or  14  Pis.  24  X  f  X  9'-10|". 


PI.  (or  Pis.) :     width :    thickness :     length 

(inches)  (inches)         (feet  and  inches) 


43 


44 


PART   II  —  STRUCTURAL   DRAFTING 


Note  that  the  width  is  across  the  grain,  while  the  length  is  along  the 
grain.     See  IX-(9),   page   76  :  1.     If   possible,   plates  of  even  width, 

i.e.,  whole  inches  without  fractions,  should 
be  chosen  in  order  that  stock  sizes  may  be 
used  without  being  recut. 


Fig.  44.  Usually  the  width  is  the  smaller  dimension,  but 

this  may  be  reversed  in  case  the  longer  dimension 

can  be  made  a  stock  width  more  conveniently;   or  in  case  material  may  be  saved  by 
cutting  several  plates  as  shown  in  Fig.  44. 

When  plates  are  used  as  fillers  the  PI.  or  Pis.  is  replaced  by  Fill,  or 
Fills.  For  other  special  abbreviations  used  in  plate  work  see  page 
45  :  7.  For  the  areas  and  the  weights  of  plates  see  page  321. 

1.  Angles: 
Number:      L(orLs):     longer  leg:     shorter  leg:     thickness:    length 


(pieces) 


(inches) 


(inches) 


(inches)     (feet  and  inches) 


Thus:  1  L  6  X  4  X  i  X  7J,  or  12  U  3  X  2J  X  A  X  10'-6". 

In  the  offices  of  some  companies,  the  angle  sign  (|_)  is  placed  after 
the  thickness,  thus:  8-5  X  3J  X  f  Ls-18'-3".  For  special  abbreviations 
used  for  angles  see  page  45  :  7.  For  the  weights  and  the  dimensions 
of  angles  see  page  303. 

2.  I-beams : 

Number:       depth:       I  (or  Is):       weight:  length 

(pieces)  (inches)  (pounds  per  foot)      (feet  and  inches) 

Thus:  one  12"  I  31|#  18'-0",  or  2'-15"  Is  42#  25'-7^"- 
Note  that  if  there  is  only  one  piece  the  number  is  spelled  "one,"  but 
if  more  than  one  piece  the  number  is  expressed  in  figures.  This  obviates 
ambiguity  between  1-8"  I,  and  18"  I,  etc.,  when  poorly  executed  or 
indistinctly  printed.  For  the  weights  and  the  dimensions  of  I-beams 
see  pages  298  and  299. 

3.  Channels: 

Number:         depth:        LJ(orLsj):       weight:  length 

(pieces)  (inches)  (pounds  per  foot )       (feet  and  inches) 

Thus:  one  12"  u  20i#  12'-10",  or  7-8"  UJ  111#  15'-1H". 

Note  that  if  there  is  only  one  piece  the  number  is  spelled  "one,"  but 


if  more  than  one  piece  the  number  is  expressed  in  figures,  as  in  I-beams. 
Note  also  that  the  channel  sign  (l_j)  is  made  preferably  with  the  web 
horizontal  to  diminish  the  liability  of  confusion  with  the  I-beam  (I)  if 
poorly  made.  A  special  interpretation  is  given  to  different  ways  of 
making  this  sign  on  floor  plans.  See  page  157  :  2.  For  the  weights 
and  the  dimensions  of  channels  see  pages  300  and  301. 


rod  (or  rods) :       length 

(feet  and  inches) 


4.  Rods: 

Number:     diameter  or  side:     °  or 

(pieces)  (inches) 

Thus:  l-f"0  rod  12'-0",  or  10-l"a  rods  ll'-Of". 

Note  that  a  circle  (  )  is  used  for  round  rods  and  a  square  (D)  for 
square  rods. 

5.  Tees: 

Number  :  T  (or  Ts)  :  width  of  flange :  length  of  stem :  weight : 


(pieces) 


(inches) 


(inches) 


(pounds  per  foot)  (feet  and  inch 


Thus:  1  T  3  X  3|  X  8.6#  X  12'-11",  or  3  Ts  4  X  3  X  9.3#  X  13'-2". 
Note  the  distinction  between  a  3  X  3|    (3"   flange)   and   a 
(3"  stem),  etc. 

6.  Z-bars: 

Number:-   Z(orZs):     depth:     width  of  flanges:     thickness:     length 

(pieces) 

Thus:  1  Z  6  X 

7.  Rails: 

Number:     Rail  (or  Rails):     weight:     standard:     length 


(inches)  (inches)  (inches)       (feet  and  inch 

X  -ft  X  8'-3l",  or  4  Zs  3TV  X  2f  X  ,5ff  X  17'-0". 


(pieces) 


(pounds  per  yard) 


(feet  and  inches) 


Thus:  1  Rail  85  #/yd.  A.S.C.E.  20'-0",  or  16  Rails  100  #/yd.  A.R.E.A. 
33'-0".  Note  that  the  weights  of  rails  are  given  in  pounds  per  yard, 
instead  of  pounds  per  foot  as  in  the  case  of  other  shapes;  for  this  reason 
it  is  preferable  to  write  the  weight  as  above,  although  the  (#/yd.)  is 
often  written  simply  (#).  The  standards  of  the  American  Society  of 
Civil  Engineers,  the  American  Railway  Engineering  Association,  and 
the  American  Railway  Association  are  in  common  use.  The  usual 


CHAPTER    VII 


THE   CONVENTIONAL   METHODS   OF   BILLING 


45 


lengths  arc  30  ft.  for  rails  up  to  60  #/yd.  and  33  ft.  for  the  heavier  rails. 
For  the  dimensions  and  the  properties  of  rails  see  page  317. 
1 .   Eye  bars : 

Number  :  eve  bar  (or  eve  bars)  :  width  of  main  bar  :  thickness  : 

of  holes 


(pieces) 


(inches) 


(inches 


(feet  and  inches) 


.   Thus:    1  eye  bar  14  x  1  X  lo'-O"  c.  to  c.  of  holes,  or  2  eye  bars  8  X 
-J  X  12'-0"  c.  to  c.  of  holes. 

Note  that  the  lengths  of  eye  bars  are  given  from  center  to  center  of 
pin  holes  instead  of  the  extreme  length. 

Eye  bars  are  connected  by  means  of  pins.  The  distances  from  center  to  center  of 
pins  are  calculated,  and  the  eye  bars  should  be  made  to  correspond.  The  heads  of  the 
eye  bars  are  upset  while  hot,  and  the  holes  are  then  sub-punched,  i.e.,  punched  to  a 
smaller  diameter  than  the  required  size.  Two  boring  machines  are  carefully  set  so 
that  the  finished  holes  at  both  ends  of  a  bar  can  be  bored  simultaneously  at  the  exact 
specified  distance  apart.  The  over-all  length  is  therefore  relatively  unimportant. 

2.  Lattice  bars : 

Number:    Latt.  bars:   width:    thickness:    length  c.  to  c.  of  holes 

(pieces)  (inches)  (inches)  (feet  and  inches) 

Thus:  22  Latt.  bars  2\  X  J  X  l'-2f"  c.  to  c. 

Note  that  the  lengths  of  lattice  bars  are  given  from  center  to  center 
of  rivet  holes.  Since  this  is  not  in  accord  with  the  method  of  billing 
other  material,  the  lengths  should  always  be  followed  by  "  c.  to  c." 

The  distance  center  to  center  of  holes  is  much  more  important  than  the  extreme 
length  in  order  to  insure  an  accurate  matching  of  the  holes.  Furthermore,  this  dis- 
tance is  used  in  setting  the  adjustable  stop  in  a  special  lattice  bar  punch.  This 
machine  cuts  out  the  material  between  the  curved  ends  of  two  bars  and  punches  the 
holes  in  these  ends  simultaneously  according  to  standard  dies,  as  indicated  on  page 
315.  As  the  bar  is  advanced  to  the  adjustable  stop  and  punched  again,  a  complete 
lattice  bar  is  made  at  a  single  stroke. 

3.  Washers: 

Number:         washer  (or  washers) :         diameter:         thickness 

(pieces)  (inches)  (inches) 

Thus:  4  washers  1\  X  ;. 

4.  Rivets: 

Number:      diameter:      rivet  (or  rivets) :      length 

(pieces)  (inches)  (inches) 

Thus:   450-f "  rivets  \\"  long. 


If  rivets  have  countersunk  heads  the  fact  should  be  stated.  The 
diameter  of  a  rivet  is  the  diameter  of  its  shank  (page  30  :  4).  The 
length  of  a  button  head  rivet  is  from  the  underside  of  the  head  to  the 
end.  The  length  of  a  countersunk  rivet  is  the  extreme  length,  includ- 
ing the  thickness  of  the  head  (page  304).  The  number  and  the 
lengths  of  rivets  are  seldom  specified  except  on  the  rivet  lists  from 
which  the  field  rivets  are  made  and  shipped.  The  size  of  shop  rivets 
is  given  on  structural  drawings  thus:  f"  rivets. 

5.   Bolts: 

Number:       bolt  (or  bolts) :      diameter:       length 


(pieces) 


(inches) 


(feet  and  inches) 


Thus:  2  bolts  \  X  2,  or  4  bolts  1"  X  l'-3"  Ig. 

If  a  bolt  has  a  countersunk  head  the  fact  should  be  stated.  The 
diameter  of  a  bolt  is  the  diameter  of  its  shank  (page  304).  The 
length  of  an  ordinary  bolt  is  from  the  underside  of  the  head  to  the  end. 
The  length  of  a  countersunk  bolt  is  the  extreme  length,  including  the 
thickness  of  the  head. 

6.  Holes: 

Diameter:     hole  (or  holes) 

(inches) 

Thus:  \l"  holes. 

Rivet  holes  are  made  -fa"  larger  than  the  diameter  of  the  rivets  to  be 
inserted.  (Why?  See  page  30:4.)  Most  bolt  holes  in  structural 
work  are  made  TV"  larger  than  the  corresponding  bolts,  except  holes 
for  anchor  bolts  (pages  73  :  3  and  106  :  5). 

7.  Special  Abbreviations.  —  Adjectives  may  be  used  before  the  abbre- 
viations for  plates  and  angles  to  aid  in  identification,  as  for  example:  — 

Bear.  PI.  for  bearing  plate, 

Bent  PI.  for  bent  plate, 

Cov.  PI.  for  cover  plate, 

Fl.  PI.  for  floor  plate, 

Reinf.  PI.  for  reinforcing  plate, 

Spl.  PI.  for  splice  plate, 

Web.  PI.  or  Web  for  web  plate, 

Flge.  L.  for  flange  angle. 

Spl.  L.  for  splice  angle, 

Stiff.  L.  or  Stiff  for  stiffening  angle. 


CHAPTER  VIII 


STRUCTURAL  DRAWINGS  — THE  DIMENSIONS 

SYNOPSIS:  Structural  steel  cannot  be  trimmed  and  fitted  during  erection  as  wood  is 
cut  in  carpentry,  but  all  parts  of  a  structure  must  be  made  to  fit  the  first  time.  Conse- 
quently, more  elaborate  precautions  must  be  taken,  first  to  insure  the  correctness  of 
all  dimensions,  and  second  to  make  sure  that  the  dimensions  are  so  expressed  on  the 
drawing  that  they  cannot  be  misunderstood.  In  few  kinds  of  work  is  there  a  more 
exacting  system  of  painstaking  precautions  and  checks  than  in  the  work  in  a  modern 
structural  drafting  room.  The  drawings  must  be  issued  absolutely  free  from  mis- 
takes, as  far  as  possible,  for  each  uncorrected  mistake,  unless  detected  in  the  shop, 
may  cause  the  loss  of  a  large  sum  of  money.  (For  example,  the  use  of  30'-0"  instead 
of  30'-6"  for  the  lengths  of  1200  I-beams  once  caused  a  large  loss.)  In  this  chapter 
are  given  rules  and  suggestions  for  dimensioning  a  structural  drawing,  including  the 
use  of  the  dimension  lines,  the  arrow  heads,  and  the  figures. 


1.  In  this  book  a  distinction  is  made  between  the  terms  "  dimen- 
sion "  and  "  size."     The  former  implies  the  use  of  a  dimension  line 
upon  which  the  dimension  is  written,  whereas  the  "size  "  applies  to  the 
figures  which  are  used  in  billing  (Chapter  VII,  page  43),  and  may  refer 
to  the  depth,  the  width,  the  thickness,  the  weight,  the  length,  or  to 
various  combinations  of  them. 

2.  The  dimensions  form  one  of  the  principal  parts  of  the  working 
drawing.     The  shopmen  and  the  draftsmen  who  use  the  finished  draw- 
ings are  never  permitted  to  scale  them,  but  must  always  use  the  figured 
dimensions.     It  is  therefore  important  that  all  dimensions  should  be 
accurate,  and  the  extent  of  each  dimension  should  be  apparent.     A 
dimension  is  worthless  unless  it  is  of  some  use,  unless  it  is  perfectly 
legible,  and  unless  there  is  no  ambiguity  regarding  the  two  points  be- 
tween which  it  is  intended. 

3.  Dimensions  should  indicate  the  actual  measurements  of  the  piece 
represented,  regardless  of  the  scale  used  in  the  drawing. 


4.  The  dimensions  should  be  placed  upon  the  drawing  as  soon  as 
determined,  while  fresh  in  mind.      The  dimensions  should  usually  be 
determined  in  the  order  of  importance,  the  main  dimensions  first,  and 
those  for  the  details  last.     The  main  dimensions  for  a  drawing  are 
generally  determined  from  the  erection  diagrams  or  the  design  sheets, 
while  the  dimensions  for  the  details  are  found  in  the  tables  of  this  book, 
in  the  handbooks  or  the  standards  of  the  different  steel  or  structural 
companies,  or  else  they  are  supplied  by  the  draftsman. 

5.  Position.  —  Each  dimension  should  be  placed  upon  the  drawing  in 
such  a  manner  that  it  will  be  of  most  use  to  those  who  read  the  drawing. 
The  principal  dimension  should  be  made  conspicuous  by  being  placed 
upon  a  dimension  line  which  intersects  the  fewest  possible  number  of 
other  lines.     Thus  the  longest  dimensions,  such  as  over-all  lengths  and 
extreme  depths,  should  be  placed  on  dimensions  lines  which  are  farthest 
from  the  view  to  which  these  dimensions    apply   (usually  the    front 
view),  and  the  shorter  dimensions,  such  as  those  for  rivet  spacing  and 


46 


CHAPTER  VIII 


THE   DIMENSIONS 


47 


other  subdivisions,  should  be  on  dimension  lines  nearest  the  view.  In 
this  way  the  lines  for  long  dimensions  are  not  crossed  by  the  perpen- 
dicular projection  lines  which  mark  the  ends  of  shorter  dimensions. 
When  there  are  several  dimension  lines  close  together,  it  is  often  de- 
sirable to  make  the  figures  of  the  principal  dimension  larger  and  bolder 
than  the  rest. 

1.  Dimension  lines  should  be  continuous  black  lines,  as  fine  as  prac- 
ticable   without    appearing    ragged    (page   37:1).     They    should    be 
drawn   parallel  to  the   measurements  to  be  dimensioned,   and   should 
extend  between  projection  lines  drawn  at  right  angles  to  the  dimension 
lines  to  indicate  the  distances  intended. 

2.  Dimension  lines  should  usually  be  placed  outside  of  the  view 
dimensioned,  and  preferably  between  the  views  if  more  than  one.     At 
times,  however,  a  few  dimensions  may  be  placed  in  a  clear  part  of  the 
view  itself  if  space  or  clearness  is  gained  thereby. 

3.  Dimension  lines  are  usually  placed  about  J"  apart,  although  this 
may  be  reduced  to  fV'  or  increased  to  TV',  depending  upon  the  available 
space.     The  distance  from  the  view  to  the  nearest  dimension  line  is 
made  twice  the  space  between  dimension  lines,  unless  it  must  be  in- 
creased to  allow  for  projecting  details,  or  for  other  shorter  dimension 
lines. 

4.  Arrow  heads  should  be  placed  on  the  dimension  lines  to  indicate 
the  extent  of  the  dimensions.     They  should  be  made  definite,  otherwise 

the  dimensions  are  useless.  The  size  and  the  style  of  arrow 
~a  heads  depend  upon  their  location.  For  main  overall  dimen- 
—  b  sions  they  may  be  made  large  and  bold,  as  in  Fig.  47  (a). 

c    Flat  curved  arrow  heads  appear  more  graceful  and  may  be 

used  wherever  there  can  be  no  ambiguity,  Fig.  47  (6),  but 
when  a  dimension  extends  to  one  of  two  lines  which  are  close 
9    together,  the  arrow  heads  should  be  made  short  and  wide, 
Fig.  47.      so  that  the  vertex  is  distinct.     See  Fig.  47  (c).     They  should 
not  be  made  large  when  close  together.     Arrow  heads  gener- 
ally point  away  from  the  dimension  figures,  but  in  narrow  spaces  they 
may  be  reversed.     See  Fig.  47  (d).     A  dimension  extends  from  the  vertex 
of  one  arrow  head  to  the  vertex  of  the  first  arrow  head  in  the  opposite 
direction.     Usually  only  one  dimension  is  placed  between  these  arrow 


heads  and  this  should  be  placed  midway  between  them  (except  extension 
figures,  page  86  :  5). 

5.  Dimension  figures  should  be  made  large  and  distinct.     Words  if 
illegible  can  sometimes  be  guessed,  but  figures  never.     Each  digit  should 
be,  carefully  drawn  or  printed,  not  hastily  made  as  in  computation. 
Beginners  have  a  tendency  to  make  the  figures  too  small  or  with  too 
thin  lines;  they  appear  still  thinner  if  not  entirely  illegible  on  the  blue- 
print.    Figures  made  with  a  crow-quill  pen,  for  example,  are  altogether 
too  light.     Simple  figures  should  be  made;    curves  should  be  avoided 
where  straight  lines  can  be  used,  thus: 

I  noil,     2  not  2,     3  not  3,     4  not  4,     5  not  5. 

6.  Dimension  figures  should  usually  be  placed  just  above  the  dimen- 
sion lines.     This  practice  differs  from  the  system  employed  in  machine 
drawing,  where  the  figures  are  placed  in  breaks  in  the  lines.     In  struc- 
tural drafting  much  time  is  saved  by  drawing  the  dimension  lines  the 
full  length,  and  then  subdividing  them  into  the  required  number  of  parts 
at  will,  particularly  if  this  number  is  large.     Dimensions  should  never 
be  placed  upon  lines  which  are  used  for  other  purposes,  as  for  example, 
main  lines  of  the  drawing,  center  lines,  rivet  lines,  or  projection  lines 
for  dimensions  at  right  angles  to  the  ones  in  question. 

7.  Fractions  should  be  made  with  the  lines  horizontal,  never  inclined. 
Thus,  not  only  is  space  economized,  and  the  general  appearance  of  the 
drawing  improved,  but  many  serious  mistakes  are  obviated;    for  ex- 
ample, /  1/16  might  be  either  eleven-sixteenths  or  one  and  one-sixteenth. 
The  figures  of  fractions  should  be  nearly  as  large  as  the  whole  numbers, 
instead  of  one-half  as  high.     If  a  figure  of  a  whole  number  should  be  of 
a  certain  size  to  be  clearly  legible,  it  is  equally  important  that  each  figure 
of  a  fraction  should  be  of  this  size. 

8.  Mistakes.  —  If  a  wrong  figure  is  made  it  should  be  erased  entirely 
and  a  correct  figure  should  be  made  in  its  place.     A  correct  figure  should 
never  be  superimposed  on  an  incorrect  figure,  even  if  made  heavier, 
for  the  man  in  the  shop  may  not  know  which  is  correct ;  neither  should 
the  first  figure  be  crossed  out  and  a  new  one  written  above  it. 

This  is  contrary  to  the  usual  practice  in  keeping  field  notes  in  surveying  in  which  a 
line  is  drawn  through  an  incorrect  measurement  and  the  correct  value  written  just 


48 


PART  II --STRUCTURAL  DRAFTING 


above.  '  In  surveying  this  indicates  to  the  man  who  plots  the  notes  that  the  measure- 
ment was  repeated,  which  fact  may  prove  of  value  when  the  notes  are  adjusted.  In 
structural  work  the  drawings  are  used  only  by  men  who  are  interested  in  the  correct 
values,  and  nothing  can  be  gained  by  exposing  the  draftsman's  mistakes. 

1.  When  the  space  between  the  arrow  heads  is  so  limited  that  Jhe 
dimension  figures  cannot  be  placed  on  the  drawing  in  the  usual  man- 
ner, it  is  frequently  possible  to  compress  the  figures  laterally  without 
reducing  their  height,  thus  making  little  apparent  alteration,  as  shown 
in  Fig.  47  (d).     In  case  this  method  cannot  be  adopted  the  figures  can 
be  placed  either  below  the  line  betwe«n  the  arrow  heads,  or  else  a  little 
to  one  side  with  an  arrow  leading  to  the  corresponding  space,  as  shown 
in  Fig.  47  (e).     In  all  cases  the  figures  should  be  made  parallel  to  the 
dimension  line. 

2.  All  figures  and  notes  should  be  arranged  so  that  they  can  be  read 
from  the  bottom  edge  or  from  the  right-hand  edge  of  the  sheet,  or  from 
a  position  between  the  two;  i.e.,  the  lettering  should  read  from  the  left 
toward  the  right  or  from  the  bottom  toward  the  top.     Draftsmen  soon 
become  so  familiar  with  figures  and  notes  in  these  positions  that  they 
can  read  them  all  without  turning  the  sheet.     On  lines  which  slope 
upward  to  the  left  and  downward  to  the  right,  particularly  on  lines 
which  are  more  nearly  vertical  than  horizontal,  the  direction  of  the 
lettering  is  not  so  rigidly  determined  by  a  general  rule  but  is  left  to  the 
judgment  of  the  draftsman.     If  the  sloping  dimensions  of  a  member 
are  used  in  conjunction  with  vertical  dimensions  more  than  with  hori- 
zontal ones,  it  is  often  more  convenient  to  have  the  figures  read  from 
the  bottom  toward  the  top;   otherwise,  it  is  better  to  print  them  from 
the  left  toward  the  right  so  that  they  can  be  read  from  the  bottom  of  the 
sheet  without  turning  the  drawing. 

3.  All  dimensions  should  be  expressed^  in  feet  and  inches  and  fractions 
of  inches.     The  fractions  should  be  reduced  to  the  simplest  form  thus: 
f  not  i£.     Usually  no  dimension  should  be  used  in  structural  drafting 
which  is  not  a  multiple  of  one-sixteenth  of  an  inch ;  in  fact  it  is  desirable 
to  avoid   fractions  in   sixteenths  wherever  possible,   as   explained   on 
page  34  :  6. 

4.  Decimals  should  be  avoided  in  dimensions.     Decimals  from  the 
handbooks  should  be  converted  into  fractions,  either  by  means  of  a 


table  (page  333)  or  mentally.  Approximately,  0.06  —  1'ff,  and  this 
gives  the  correct  result  if  referred  to  the  nearest  quarter  of  an  inch,  as 
for  example:  —  0.81  is  0.06  more  than  0.75,  hence  ^  +  f  =  \%;  and 
0.19  is  0.06  less  than  0.25,  hence  i  —  A  =  iV  If  a  web  thickness  given 
in  decimal  form  should  fall  midway  between  sixteenths,  the  higher 
sixteenth  is  usually  chosen  in  dimensioning  to  allow  for  "packing," 
since  paint,  scale,  bends,  etc.,  do  not  permit  the  surfaces  of  two  pieces 
to  be  brought  into  perfect  contact.  The  tables  at  the  end  of  this  book 
express  the  web  thicknesses  in  both  decimal  and  fractional  forms. 

5.  The  abbreviations  (ft.)  and  (ins.)  are  not  used  in  dimensioning. 
A  single  accent  mark  (')  represents  feet,  and  a  double  accent  (")  inches. 
Dimensions  less  than  one  foot  are  usually  expressed  in  inches  alone,  but 
to  avoid  ambiguity  dimensions  of  one  foot  or  over  (even  if  even  feet) 
should  always  show  both  feet  and  inches  with  hyphens  between. 


Note:  The  width  of  a  plate  is  given  in  inches  when  billed  (page  43  :  3),  whether 
more  or  less  than  12",  but  when  given  as  a  dimension  with  a  dimension  line  it  is  expressed 
in  feet  and  inches  if  I'-O"  or  over.  Hence  it  is  no  exception  to  the  general  rule. 

The  inch  marks  (")  of  dimensions  less  than  one  foot  may  often  be 
omitted,  provided  there  can  be  no  doubt  as  to  the  meaning;  but  the 
inch  marks  should  be  used  whenever  the  drawing  can  be  made  more 
clear  thereby.  The  correct  method  of  writing  dimension  figures  can 
best  be  shown  by  examples,  as  follows:  — 


Correct 

i 

2",  or  61 

I'-O" 

2'-0" 

3'-4i" 

4'-Of" 


Incorrect 


not 
not 
not 
not 
not 
not 


Oi 


0'-2",  or 
1'  or  12" 
2' 
3'-04i" 


4'-f",    or   4'-00|" 


6.  Recurring  Dimensions.  —  Ditto  marks  (")  should  never  be  us 
in  place  of  dimensions.  The  use  of  arrows  leading  from  one  figure  to 
two  or  more  spaces  should  be  avoided.  Like  dimensions  should  be 
repeated  at  every  occurrence,  unless  grouped  as  explained  on  page 
49  :6. 


CHAPTER  VIII 


THE   DIMENSIONS 


49 


2} 


?|.  4  ®3". 


I'D'' 


we 


*©-e — e-s-©n©-< 


eeo — e-e-e- 


Fig.  49. 


1.  A  dimension  which  is  clearly  given  in  one  view  should  not  be 
repeated  in  another,  for  it  usually  complicates  the  drawing  unneces- 
sarily, and  causes  trouble  if  one  is  changed. 

2.  Rivets  and  holes  should  be  located  by  dimensions  which  extend 
to   their   centers.     They   should   be   dimensioned   in   the   views   which 
show  them  as  circles,  although  exceptions  to  this  rule  are  occasionally 

allowed  in  order  to  dispense  with  additional 
views  (page  91  :  4).  "Staggered  rivets," 
i.e.,  rivets  which  alternate  on  two  lines, 
should  be  dimensioned,  not  diagonally,  but 
parallel  to  the  rivet  lines  as  if  the  rivets 
were  on  a  single  line.  See  Fig.  49. 

3.  The  gages  of  all  structural  shapes 
should  be  given  in  all  cases  (except  latticed 
members,  page  136:3).  The  standard 

gages  given  in  the  tables  should  be  used,  except  in  special  cases  which 
.  are  noted  elsewhere,  as  for  example  on  pages  83  : 6, 106  :  3, 132  : 1,  132  : 3, 

136:1,  and  139:3. 

4.  The  majority  of  edge  distances  are  omitted  unless  they  are  im- 
portant.    For  example,  a  dimension  should  be  given  in  order  to  limit  an 
edge  distance  to  provide  ample  clearance  for  a  connecting  part  (page 
72  :  4),  or  to  tie  a  group  of  rivets  to  an  important  edge  to  which  a 
main   dimension    extends  (Fig.  148).     But   if    a   connection    plate    or 
angle,  or  a  web  member  of  a  truss,  is  shown  without  edge  distances,  the 
shopmen  will  make  the  distances  on  opposite  edges  equal;    with  this 
understanding  many  dimensions  may  be  omitted. 

5.  A  line  of  rivet  spacing  should  be  confined  to  dimensions  from 
'  center  to  center  of  rivets  and  holes,  except  at  the  ends  where  it  is  fre- 
'  quently  necessary  to  give  the  distance  from  the  first  rivet  to  the  end  of 

the  member  or  to  some  other  definite  point.  Intermediate  edge  dis- 
tances and  gages  should  never  be  given  on  the  same  line,  because  they 
are  not  used  at  the  same  time;  they  should  be  shown  as  separate  dimen- 
sions, usually  between  the  line  of  rivet  spacing  and  the  corresponding 
view  of  the  member.  See  Fig.  49. 

6.  Dimensions  should  never  be  given  to  the  edges  of  the  flanges  of 
structural  shapes,  but  always  to  the  backs  of  channels  and  angles,  to 


the  center  lines  of  I-beams,  and  similarly  for  other  shapes.  The  back 
of  an  angle  or  a  channel  is  a  well-defined  line,  but  the  outside  edges  are 
not  so  well  defined.  More  important  than  this,  however,  is  the  fact  that 
the  lengths  of  legs  and  the  widths  of  flanges  are  frequently  different 
from  what  they  are  supposed  to  be.  As  a  rule,  such  variation  is  of  no 
consequence  in  structural  work,  but  it  should  be  considered,  particu- 
larly in  the  case  of  thick  angles.  See  page  25  :  1.  For  illustration, 
suppose  a  girder  is  composed  of  a  f"  web  plate  and  6x4  angles. 
The  total  width  of  each  flange  is  theoretically  I'-Of",  but  if  the  angles 
should  "overrun,"  as  they  are  likely  to  do,  the  width  would  be  more. 
Ordinarily  this  increase  would  not  matter  and  for  this  reason  the 
dimension  should  not  be  given;  in  case  the  extreme  width  is  limited 
by  the  clear  distance  between  column  flanges  or  for  other  reasons,  the 
dimensions  should  be  given  with  the  understanding  that  in  case  of 
overrun,  the  outside  edges  of  the  angles  would  have  to  be  planed  —  a 
process  too  expensive  to  be  used  unnecessarily. 

It  is  unnecessary  to  give  the  widths  of  flanges  or  the  dimensions  of  fillets  and  other 
curves  which  apply  to  the  manufacture  of  the  steel  rather  than  to  the  fabrication. 
It  should  be  borne  in  mind  that  the  drawings  are  to  be  used  for  the  purpose  of  putting 
standard  shapes  together,  and  therefore  many  dimensions  may  be  superfluous  unless 
they  are  directly  related  to  shearing,  bending,  punching,  riveting  or  similar  processes. 

When  an  angle  with  unequal  legs  is  represented  in  only  one  view  it  is  often  neces- 
sary to  indicate  which  leg  is  shown.  This  may  be  noted  as  for  example  "  3"  leg, " 
but  more  frequently  the  length  of  the  leg  is  put  on  in  the  form  of  a  dimension  with  the 
understanding  that  it  is  no  more  exact  than  the  billed  length  and  that  the  angle  need 
not  be  cut  in  case  of  overrun. 

7.  When  three  or  more  spaces  are  numerically  equal  and  serve  similar 
purposes,  they  may  be  dimensioned  in  a  group,  thus:  — •  5  @  6  =  2'-6", 
or  4  @  l'-2"  =  4'-8",  or  as  some  companies  prefer,  5  of  6  =  2'-6".  If 
the  rivets  are  staggered  (page  49  :  2),  the  spaces  are  given  just  as  if 
the  rivets  were  on  the  same  line,  although  the  abbreviation  "alt.  spa." 
for  "alternate  spaces"  is  sometimes  added,  thus: —  5  alt.  spa.  @ 
6  =  2'-6".  Edge  distances  and  gages  should  not  be  combined  with 
distances  from  center  to  center  of  rivets  and  holes  in  this  method,  but 
should  have  the  dimensions  repeated,  even  though  identical.  In  the 
same  way  it  may  be  preferable  to  separate  one  or  more  of  the  spaces 
from  the  group  if  they  serve  purposes  in  addition  to  the  spacing  of 


50 


PART  II  —  STRUCTURAL  DRAFTING 


rivets  along  the  same  line  as  the  rest  of  the  group,  as  for  example,  the 
2J  and  3  inch  spaces  in  Fig.  49  which  locate  rivets  in  the  stiffening 
angles  and  splice  plates. 

1.  When  a  long  line  of  shop  rivets  and  holes  for  field  rivets  are  dimen- 
sioned in  a  single  group,  and  the  holes  occur  at  such  intervals  that  spaces 
must  be  counted  to  determine  their  location,  a  supplementary  dimen- 
sion line  may  be  added  for  the  holes  only,  as  in  the  top  flange,  Fig.  103. 

2.  If  two  or  more  lines  of  dimensions  extend  between  the  same  points. 
the  sum  of  the  dimensions  in  each  line  should  be  the  same  as  in  the 
others.     If  a  line  of  dimensions  extends  practically  the  whole  length  of 
a  member  it  is  well  to  complete  it  by  adding  one  or  more  dimensions  to 
afford  a  check  with  the  over-all  length.     This  is  of  special  benefit  to  the 
templet  maker,  who  would  otherwise  have  to  procure  his  own  total  for 
a  check. 

CHECKING  SUBDIVISIONS:  Never  complete  a  line  of  dimensions  between  two  points 
without  adding  them  to  see  if  the  sum  equals  the  proper  distance  between  those  points. 
Neglect  of  this  precaution  is  a  source  of  much  trouble. 

3.  Dimensions  should  be  placed  upon  the  drawing  in  such  a  manner 
that  the  shopmen  will  not  be  compelled  to  add  or  subtract  dimensions 
in  order  to  obtain  the  figures  they  need.     For  example,  one  hole  in  the 
connection  angle  on  the  flange  face  of  column  C5  Fig.  137,  is  tied  to  one 
rivet  in  the  other  leg  (or  else  each  could  be  tied  to  the  same  end  of  the 
angle);  otherwise,  the  templet  maker  could  not  make  the  templet  for 
the  angle  without  finding  the  total  distances  from  the  rivet  and  from  the 
hole  to  the  bottom  of  the  column  and  then  subtracting  these  two  sums. 
Similarly,  the  holes  in  the  connection  plate  pb  near  the  center  of  this  same 
column  are  dimensioned  independently  of  the  rivets;    a  line  is  drawn, 
however,  to  show  that  the  top  holes  and  rivets  are  opposite. 

4.  No  rivets  or  holes  should  be  located  by  more  than  one  method  of 
dimensioning.     They  may  be  determined  either  by  dimensions  at  right 
angles  to  each  other  (rectangular  coordinates),  or  by  "slopes  and  dis- 
tances "  (polar  coordinates),  the  slopes  of  the  rivet  lines  being  indicated 
in  the  usual  manner  (page  50  :  7)  and  the  distances  along  these  lines 
being  given.     A  combination  of  these  two  methods  is  not  only  unneces- 
sary, but  is  liable  to  cause  difficulty  in  the  shop,  for  the  points  that 


Fig.  50. (a) 


coincide  on  a  small  layout  in  the  drafting  room  might  fall  noticeably 
apart  on  the  full-sized  templet.  In  order  to  avoid  ambiguity  on  the 
drawing  in  case  a  line  which  locates  one  rivet  or  hole  happens  to  pass 
through  another  rivet  or  hole  which  is  located  in  another  way, 
the  line  should  be  made  to  pass  around  the  second  rivet  or 
hole  by  means  of  an  arc  of  a  circle,  as  shown  in  Fig.  50  (a). 
Whether  the  drawing  is  made  accurately  to  scale  or  whether 
the  line  would  actually  pass  through  the  center  or  not  is 
immaterial,  the  object  of  the  arc  being  to  show  clearly  that 
the  line  is  independent  of  the  second  rivet  or  hole. 

5.  For  field  connections  —  connections  of  different  members  in  the 
field  —  the  dimensions  on  the  drawing  of  one  member  should  be  given 
in  exactly  the  same  way  as  the  corresponding  dimensions  on  the  draw- 
ing of  the  other  member  so  that  each  person  who  uses  the  drawings 
may  see  at  a  glance  that  these  dimensions  do  correspond. 

6.  The  rivets  in  the  ends  of  the  lattice  bars  of  a  single  system  of 
latticing  are  dimensioned  in  groups  much  as  staggered  rivets  are  dimen- 
sioned (page  49  : 2) ;    each  space   is   measured   parallel   to  the  axis  of 
the  member  latticed,  from  the  center  of  the  rivet  at  one  end  of  a  bar  to 
the  center  of  the  rivet  at  the  other  end.     See  Fig.  137.     The  method  of 
dimensioning  a  double  system  of  latticing  is  the  same  as  for  a  single 
system,  the  rivet  at  the  intersection  of  each  pair  of  bars  being  shown 
but  not  dimensioned.     See  Fig.  124.     For  lattice  bars  with  two  rivets 
at  each  end,   see  Fig.  127.  ( 

7.  The  slope  of  a  line,  i.e.,  its  "bevel,"  with  reference 
to  another  line  is  given,  as  shown  in  (a)  Fig.  50  (6),  by  in- 
dicating dimensions  on  two  mutually  perpendicular  sides 
of  a  right  triangle;  the  hypothenuse  of  this  triangle  is 
either  coincident  with  or  parallel  to  the  line  whose  direc- 
tion is  to  be  given,  and  the  other  sides  are  respectively 
parallel  and  perpendicular  to  the  reference  line.  The 
dimension  on  the  longer  perpendicular  side  is  always  12", 
.vhile  the  corresponding  dimension  (in  inches  and  frac- 
tions) on  the  shorter  side  must  be  calculated.  This 
shorter  dimension  is  usually  obtained  directly  from  dimensions  between 
working  points,  as  explained  on  page  76  : 2,  without  the  necessity  oi 


(6) 


(c) 


Fig.  50  (6) 


CHAPTER  VIII 


THE  DIMENSIONS 


51 


knowing  the  actual  value  of  the  angle.  Angles  are  almost  never  given 
in  degrees  and  minutes  on  structural  drawings  but  the  corresponding 
slopes  are  used. 

A  workman  in  the  shop  usually  has  no  such  means  as  an  accurate  protractor  for 
laying  off  angles,  but  he  must  work  with  a  two-foot  rule,  a  steel  tape,  or  other  device 
for  laying  off  linear  measurements. 

Parts  of  trusses  or  bracing  systems  are  often  laid  out  on  the  floor  of 
the  templet  shop  from  the  main  dimensions  instead  of  on  the  bench,  pro- 


vided that  the  extreme  dimensions  do  not  exceed  30  or  40  feet.  If  the 
dimensions  between  working  points  are  not  clearly  shown  on  the  draw- 
ing they  may  be  given  on  the  triangle  without  being  reduced  to  a  base 
of  12",  as  shown  in  (6)  Fig.  50  (6).  The  two  schemes  may  be  combined  as 
in  (c)  Fig.  50  (6)  in  order  to  show  the  dimensions  between  working  points 
for  the  convenience  of  the  checker,  and  the  corresponding  reduced 
dimensions  for  use  in  the  shop.  This  method  may  be  used  when  a 
draftsman  is  in  doubt  as  to  whether  the  work  will  be  laid  out  on  the 
floor  or  on  the  bench. 


CHAPTER   IX 


STRUCTURAL  DRAWINGS  —  THE  NOTES,   THE  TITLE,   AND 

THE   BORDER 

SYNOPSIS:  Structural  drawings  are  made  as  self-explanatory  as  possible  without 
supplementary  notes,  although  notes  can  often  be  used  to  advantage.  Some  of  the 
more  common  notes  are  discussed  in  this  chapter,  and  suggestions  are  given  for  making 
titles  and  borders. 

THE  NOTES 


1.  Drawings  should  be  made  complete  and  clear  without  the  use  of 
notes  whenever  practicable,  but  unless  the  drawing  is  perfectly  clear, 
short  and  concise  notes  should  be  added  wherever  necessary.     Care 
should  be  taken  to  make  each  note  explicit  and  easily  understood. 

2.  All  general  notes  which  apply  to  the  whole  drawing  should  be 
placed  near  the  title,  usually  to  the  left,  as  in  Fig.  98.     Examples  of 
the  more  common  general  notes  are  those  which  give  the  sizes  of  rivets, 
holes,   and  washers,   the   maximum   pitch  of  rivets,   and   information 
regarding  specifications,  paint,  inspection,  and  erection. 

3.  All  other  notes  should  be  placed  in  clear  spaces  near  those  parts 
of  the  drawing  to  which  they  apply.     If  a  note  is  too  long  for  the  avail- 
able space,  it  may  be  placed  to  one  side  with  a  reference  to  it  at  the 
proper  point,  as  for  example,  "See  note."     If  more  than  one  such  case 
occurs  on  one  sheet,  the  notes  may  be  numbered  or  lettered. 

4.  If  the  rivets  and  holes  for  any  drawing  are  not  all  of  the  same 
size,  the  general  note  (see  above)  should  be  modified  thus:    "Rivets 
f"  except  as  noted,"  or  "Holes  ^f"  unless  noted"   (Fig.   104).     All 
rivets  or  holes  of  sizes  other  than  those  specified  in  the  general  note 
should  be  clearly  noted.     Such  exceptional  rivets  or  holes  may  be  dis- 
tinguished on  the  drawing  in  one  of  several  ways,  thus:    (a)  by  placing 
the  note  at  one  end  of  that  dimension  line  which  locates  all  the  rivets 
or  holes  in  question  but  no  others,  as  in  P6,  Fig.  90;   (b)  by  drawing 


52 


supplementary  lines  with  arrows  to  indicate  the  desired  rivets  or  holes, 
as  in  ME,  Fig.  117,  or  FIO,  Fig.  147;  (c)  by  drawing  arrows  from  the 
note  to  those  rivet  lines  which  pass  through  all  the  rivets  or  holes  noted 
but  no.  others,  as  in  the  bottom  view,  Fig.  135;  (d)  by  encircling  the 
desired  rivets  or  holes  by  a  freehand  loop  or  ring  which  in  turn  is  connected 
to  the  note,  as  in  the  top  view,  Fig.  135;  this  ring  should  not  include  any 
dimensions  or  notes  (page  181 : 1) ;  (e)  by  noting  all  the  rivets  or  holes  in  one 
view  by  a  special  note  near  the  view  as  in  BIG,  Fig.  92,  or  by  a  general 
note  near  the  title  as  in  Fig.  99.  In  order  to  attract  attention  to  a  change 
of  size,  the  American  Bridge  Company  has  adopted  the  use  of  a  heavy 
triangle  as  illustrated  in  most  of  the  figures  referred  to  above.  Counter- 
sunk and  flattened  rivets  are  often  noted  as  explained  on  page  40  :  6. 

5.  An  identification  mark  is  assigned  to  each  member  which  is  to  be 
shipped  separately.     If  more  than  one  drawing  appears  on  a  sheet  the 
identification  mark  should  be  placed  conspicuously  near  the  drawing  of 
the  corresponding  member.     For  further  description  of  such  "Shipping 
Marks,"  see  page  80  :  6. 

6.  The  number  of  pieces  to  be  made  from  each  drawing  should  be 
clearly  stated,  either  under  the  detail,  as  in  beam  work  (Fig.  87),  or  at 
the  right  of  the  sheet  above  the  title  (Fig.  100).     When  more  than  one 
or  two  members  are  shown  on  one  sheet  a  tabular  "Required  List  "  is 
made,  as  shown  in  Fig.  147. 


CHAPTER  IX 


THE   NOTES,  THE  TITLE,  AND   THE  BORDER 


53 


1.  Reference  to  other  drawings  may  be  made  in  order  to  save  the 
repetition  of  details.     Usually  reference  is  not  made  to  another  sheet 
unless  a  system  of  assembling  marks  is  used,  as  discussed  more  fully 
on  page  79  :  2.     The  size  of  all  material  should  be  given  on  each  sheet, 
and  also  the  spacing  of  all  holes  for  field  connections  to  facilitate  com- 
parison with  the  drawings  of  connecting  members.     The  outline  of  all 
material  should  be  completely  shown  in  at  least  one  view  to  prevent 
the  shopmen  from  overlooking  a  whole  connection  or  other  detail.     The 
shop  rivets  and  the  dimensions  which  locate  the  shop  rivets  and  cuts 
may  be  referred  to  another  detail,  provided  the  latter  is  complete  in 
every  respect  without  further  reference  to  a  third  detail. 

2.  Loose  Pieces  Bolted.  —  Small  pieces,  such  as  splice  plates,  fillers, 
or  connection  angles,  which  cannot  be  riveted  in  the  shop  without  com- 
plicating the  field  work,  may  either  be  shipped  separately,  or  else  bolted 
for  shipment  to  one  of  the  members  to  which  they  are  eventually  to  be 
attached.     The  latter  method  is  to  be  recommended  wherever  feasible, 
for  the  number  of  items  shipped  is  reduced,  and  the  pieces  are  available 
at  once  when  needed  for  erection.     Pieces  which  are  bolted  for  'ship- 
ment are  fastened  temporarily  in  or  near  their  final  positions  by  means 
of  two  or  more  bolts  each.     On  the  drawing,  a  note  should  be  placed 
immediately  following  the  billed  size  of  any  piece  so  bolted,  thus:  "Bolt 
for  shipment,"  or  "Bolt  to  ship."     See  Fig.  125.     It  is  well  to  give  each 
piece  a  separate  mark  for  identification  in  case  it  becomes  detached 
unless  the  nature  of  the  piece  is  such  that  its  proper  position  can  be 
readily  determined. 

The  temporary  bolts  used  are  of  odd  lengths  as  picked  up  in  the  shop;  sufficient 
washers  are  added  to  facilitate  tightening  and  removing  the  bolts. 

To  avoid  handling  loose  pieces  in  the  field  it  is  often  feasible  to  make  them  enough 
longer  so  that  they  can  be  riveted  in  the  shop  independently  of  the  field  connections 
(Fig.  160) ;  this  should  never  be  done,  however,  if  the  erection  is  rendered  more  diffi- 
cult thereby. 

3.  In  case  pieces  are  to  remain  bolted  in  the  completed  structure 
without  having  the  bolts  replaced  by  rivets  in  the  field,  all  the  holes 
should  be  filled  with  permanent  bolts  of  the  proper  size.     The  bolts 
should  be  billed  on  the  drawing  in  the  usual  way  (page  45  :  5),  directly 
under  the  billed  size  of  the  piece  bolted.     See  Fig.  133.     A  note,  "Bolt 


complete  "  may  be  added  to  insure  the  use  of  a  full  number  of  bolts 
of  the  proper  length,  instead  of  a  few  temporary  bolts  (see  above).  The 
bolt  heads  are  sometimes  drawn  but  ordinarily,  for  the  sake  of  simplicity, 
only  the  holes  are  indicated  (page  41  :  2). 

4.  Different   Members    Combined.  —  When  several   members    differ 
from  each  other  slightly,  i.e.,  in  minor  details,  one  drawing  may  be 
made  to  represent  all  of  these  members  and  the  differences  may  be 
stated  in  notes.     This  should  not  be  done,  however,  unless  the  differ- 
ences can  be  made  clear  and  definite  in  notes  which  are  brief  and  com- 
paratively few  in  number;   otherwise,  drawings  become  so  complicated 
that  more  time  is  lost  by  the  shopmen  than  is  saved  by  the  draftsmen. 
This  is  often  due  to  the  fact  that  additional  connections  are  discovered, 
or  the  design  is  changed,  after  the  drawing  is  started.     It  is  essential, 
therefore,  to  plan  any  combination  very  carefully  before  the  drawing 
is  commenced,  using  a  sketch  upon  which  are  indicated  the  various 
connections.     The  notes  regarding  special  connections  follow  the  corre- 
sponding billed  material,  if  any;  otherwise,  the  holes  may  be  noted  as 
indicated  on  page  52  :  4.     If  there  are  more  than  a  few  simple  differ- 
ences, it  is  better  either  to  draw  an  additional  view  (Fig.  137),  or  to 
make  another  drawing.     In  the  latter  case  it  may  be  possible  to  show 
on  one  drawing  simply  the  outlines  of  all  parts  which  are  like  those  on 
the  other,  and  to  draw  in  detail  only  those  parts  which  are  different 
(Fig.  117).     In  order  to  shorten  notes,  when  several  different  members 
are  represented  by  the  same  drawing,  one  member  may  be  referred  to 
another  after  the  shipping  mark,  as  for  example:  —  "(712,  same  as  Cll 
except  as  noted,"  it  being  understood  that  every  note  which  applies  to 
Cll  applies  also  to  C12.     The  mark  "C12  "  will  not  appear  in  any  of  the 
notes,  therefore,  except  where  it  differs  from  Cll.     See  also  page  81:  3. 

5.  All  notes  should  be  made  positive,  except  in  rare  instances.     This 
precludes  the  use  of  the  word  "omit."     For  example,  if  several  mem- 
bers are  represented  by  one  sketch,  and  some  of  the  details  are  on  part 
of  the  members  only,  as  the  holes  for  rods  in  MN,  Fig.  117,  it  is  better 
to  note  that  the  holes  are  "in  MNl,  and  MN2"  rather  than  that  they 
are  "omitted  in  MN%"     It  is  much  more  important  to  all  concerned 
in  making  a  member  to  know  which  details  are  to  be  placed  on  that 
member  rather  than  to  know  which  are  not. 


54 


PART   II  —  STRUCTURAL  DRAFTING 


THE  TITLE 


1.  A  title  is  placed  in  the  lower  right-hand  corner  of  each  full-sized 
sheet,  for  convenient  reference  and  for  use  in  classification.     This  uni- 
form position  enables  a  person  to  look  through  a  pile  of  drawings  for  a 
particular  sheet  by  merely  turning  back  the  corners.     The  title  is  com- 
posed of  two  parts,  one  of  which  refers  to  the  specific  drawing,  the  other 
to  the  company  which  makes  the  drawing. 

2.  The  first  part  of  the  title  contains  the  names  of  the  members  on 
the  sheet,  or  the  part  of  the  structure  shown;    also  the  name  of  the 
structure,  the  name  of  the  customer,  and  the  place  where  the  structure 
is  to  be  situated.     This  part  of  the  title  is  usually  made  of  freehand 
letters    about   TV    high,    of    simple    Gothic    style,    and    all    capitals. 
Elaborate   titles   should   be  avoided,  since   they  add   to  the  expense, 

'and  are  not  in  harmony  with  the  rest  of  the  drawing.  Some  com- 
panies maintain  small  presses  for  printing  the  titles  of  the  larger 
contracts. 

3.  The  second  part  of  the  title  is  more  general,  and  is  usually  printed 
by  means  of  a  press  or  placed  on  the  drawing  by  means  of  a  rubber  or 
metal  stamp.     If  the  drawing  is  made  in  the  drafting  room  of  a  struc- 
tural company,  the  title  contains  the  name  of  the  company,  and  the  name 
of  the  plant  which  fabricates  the  work;    also  blanks  for  the  initials  of 
the  man  in  charge  of  the  contract,  of  the  detailer,  of  the  tracer,  and  of 
the   checker,   together  with   the   date   of  each   signature.     Additional 
blanks  are  often  left  for  the  signature  of  the  man  who  makes  a  field  check 
or  the  engineer  who  approves  the  drawing.     Below  these,  and  at  the 
extreme  bottom  of  the  sheet  next  to  the  border,  are  placed  the  contract 
number  and  the  sheet  number.     The  contract  number  should  be  made 
bold  and  conspicuous  and  in  a  uniform  position.     A  single  letter  "C  ' 
can  be  made  more  prominent  than  either  "Cont.  No."  or  "Contract 
Number  "  and  although  not  as  significant  it  has  been  found  convenient 
for  reference.     If  desired,  the  line  for  the  number  may  be  placed  opposite 
the  middle  of  the  letter,  leaving  room  for  the  sheet  number  below,  as 
shown  in  many  of  the  titles  on  the  drawings  of  this  book.     Titles  made 
in  the  offices  of  consulting  engineers  or  in  the  structural  departments  of 
railroad  or  other  companies  are  usually  somewhat  simpler  than  those 


made  in  the  offices  of  structural  companies;  in  general  they  are  similar, 
but  they  have  comparatively  few  signatures. 

4.  The  smaller  drawings  and  lists  are  usually  made  on  printed  forms 
which  contain  the  name  of  the  company  with  blanks  for  the  plant,  the 
structure,  the  nature  of  the  drawing,  the  initials  of  the  detailer  and 
the  checker,  with  dates,  and  the  contract  and  sheet  numbers  as  shown 
in  Fig.  85. 

5.  Sheet  Numbers.  —  Drawings  should  be  numbered  in  different  series 
in  order  to  facilitate  the  reference  to  a  sheet  of  a  given  number.     For 
example,  the  main  drawings  (24"  x  36")  of  a  contract  may  bear  simply 
numbers,  but  other  sheets  should  have  a  prefixed  letter  to  distinguish 
them,  thus :  E  for  erection  diagrams,  B  for  beam  details  and  other  small 
•drawings,  C  for  combination  sheets,  S  for  shop  bills,  R  for  shipping  bills, 
SR  for  combined  shop  and  shipping  bills,  EF  for  miscellaneous  lists,  etc. 


THE  BORDER 

6.  A  simple  border  should  be  drawn  on  each  full-sized  sheet  to  form 
the  boundary,  to  keep  the  sheets  of  uniform  size,  and  to  improve  the 
appearance.     Ornate  borders  should  be  avoided.     Corners  should  be 
simply  rectangular.     Borders  are  not  drawn  on  the  smaller  printed 
forms. 

7.  An  effective  border  is  composed  of  a  heavy  line  with  a  light  line 
J"    outside.     The    nominal  dimensions    of    the  sheet,  as  for  example 
24"  X  36",  indicate  the  size  of  the  finished  tracing,  and  a  rectangle  of 
this  size  should  be  penciled  to  serve  as  a  guide  in  trimming  the  doth. 
The  fine  line  is  drawn  \"  inside  of  this  to  indicate  where  the  blueprints 
are  usually  trimmed,  and  the  heavy  line  is  drawn  \"  inside  the  fine 
line  to  form  the  border  on  the  prints.     This  makes  the  dimensions 
inside  of  the  border  each  two  inches  less  than  the  nominal  size  of  the 
sheet,  as  for  example,  22"  X  34"  for  a  24"  X  36"  sheet.     If  smaller 
sheets  are  adopted,  as  for  example  15"  X  22"  for  student  use,  the  fine 
line  of  the  border  had  better  be  omitted,  the  heavy  line  only  being 
used,  \"  inside  the  edge  of  the  sheet.     In  this  case  the  tracing  cloth 
and  the  blueprints  should  both  be  cut  the  same  size  as  the  sheet  of 
paper.     The  heavy  line  should  not  be  over  7V'  wide  nor  wider  than  can 
be  drawn  with  a  single  stroke.     See  page  59:3. 


CHAPTER  X 
INKING  AND   TRACING 

SYNOPSIS:  Every  draftsman  should  cultivate  the  ability  to  ink  a  drawing  well.  Some 
men  are  naturally  more  skillful  than  others,  but  any  draftsman  can  develop  skill  with 
practice,  if  he  follows  with  reasonable  care  the  common  rules  for  inking.  Such  rules 
and  suggestions  for  inking  are  given  in  this  chapter. 


1.  Structural  drawings  are  made  primarily  for  use  in  the  shop,  and 
therefore  accuracy,  speed,  and  utility  are  of  much  more  importance  than 
appearance.     On  the  other  hand,  it  is  highly  desirable  that  a  drawing 
be  neat,  well  arranged,  and  well  executed,  although  it  is  not  so  important 
in  this  work  as  in  map  or  architectural  work.     A  good  looking  drawing 
not  only  adds  to  the  prestige  of  the  draftsman,  but  also  gives  to  all  who 
use  it  greater  confidence  in  its  accuracy.     The  appearance  of  a  drawing 
is  determined  largely  by  the  arrangement  on  the  sheet,  and  also  by  the 
skill  of  the  person  who  inks  it.     There  are  many  practical  rules  for  inking 
and  tracing  with  which  every  draftsman  should  be  familiar,  whether  he 
is  a  skilled  tracer  or  not;  by  their  adoption  he  will  be  enabled  to  make 
drawings  much  more  definite  and  useful  than  he  could  otherwise,  and  he 
will  gradually  develop  skill  along  the  proper  lines. 

2.  Three  methods  of  making  drawings  are  commonly  used.     A  draw- 
ing may  be  made  on  paper  and  then  inked ;  it  may  be  made  on  paper  and 
then  traced  in  ink  upon  tracing  cloth;  or  it  may  be  made  directly  in  ink 
on  tracing  cloth.     The  rules  for  inking  are  practically  the  same  in  all 
three  methods. 

3.  The  Care  of  Tracing  Cloth.  —  Tracing  cloth  should  never  be  folded 
or  creased,  for  permanent  cracks  would  result.     It  should  not  be  handled 
with  moist  hands,  and  water  should  not  be  allowed  to  come  in  contact 
with  it,  for  not  only  would  the  surface  be  thus  spoiled  for  inking,  but  it 
would  also  be  rendered  opaque  so  that  white  spots  would  show  on  each 
print  taken  from  the  tracing. 


4.  The  dull  or  unglazed  side  of  the  tracing  cloth  is  used  for  structural 
drawings  for  three  reasons,  viz.:  (1)  the  dull  side  is  the  only  side  upon 
which  pencil  marks  can  be  readily  made  or  erased;  not  only  is  this  of 
advantage  at  times  to  the  tracer  and  to  the  detailer  but  it  permits  the 
checker  to  note  corrections  in  pencil  directly  on  the  drawing  (page  181  : 1) ; 
moreover,  if  a  part  or  the  whole  of  a  drawing  is  to  be  made  in  pencil 
directly  on  the  tracing  cloth  (page  65  :  3)  it  must  necessarily  be  made 
on  the  dull  side;  (2)  extensive  erasures  may  be  made  with  less  apparent 
unjury  to  the  cloth  than  on  the  glazed  side,  especially  if  several  erasures 
are  made  in  one  place;  and  (3)  the  tracings  may  be  more  easily  handled 
and  filed  because  they  are  less  liable  to  curl. 

5.  Before  the  cloth  is  stretched,  the  selvage  edges  should  be  torn  off. 
These  edges  are  woven  with  the  threads  closer  together  than  in  the  body 
of  the  cloth,  and  are  not  so  susceptible  to  atmospheric  changes.     Unless 
they  are  removed,  the  cloth  is  liable  to  pucker  from  one  day  to  the  next, 
particularly  if  there  is  a  noticeable  change  in  the  amount  of  moisture  in 
the  air.     It   is  often  impossible  to  restretch  the  cloth  flat  until  the 
selvage  is  removed,  and  at  times  it  is  difficult  to  do  so  at  all;  hence  it 
is  important  to  remove  the  selvage  before  the  cloth  is  first  stretched. 
Since  the  threads  are  parallel  to  the  edges,  the  selvage  may  be  torn  off 
without  difficulty,  provided  reasonable  care  is  exercised  to  prevent  the 
cloth  from  tearing  at  right  angles  to  the  desired  direction.     The  width 
of  the  strip  to  be  removed  is  usually  apparent,  and  varies  from  J  to  J 
of  an  inch  with  the  different  makes  of  cloth.     Enough  should  be  re- 


55 


56 


PART  II  —  STRUCTURAL   DRAFTING 


moved  to  eliminate  all  the  puckers,  and  to  leave  the  cloth  perfectly 

flat. 

1.  The  cloth  should  be  tightly  stretched  over  the  drawing  to  be  traced, 
and  held  in  position  by  thumbtacks.     At  least  four  tacks  should  be  used, 
one  in  each  corner,  two  diagonally  opposite  tacks  being  placed  first. 
Additional  tacks  may  be  used,  if  necessary,  to  keep  the  cloth  taut.     The 
tracing  cloth  should  be  enough  larger  than  the  finished  drawing  to  permit 
tacking  the  cloth  to  the  board  in  such  a  manner  that  all  thumbtack  holes 
will  be  cut  off  when  the  completed  tracing  is  trimmed  to  the  proper  size. 
The  corners  of  the  cloth  may  be  folded  under  so  that  each  tack  passes 
through  two  thicknesses  of  cloth  and  is  thus  less  liable  to  tear  out.     Be- 
fore the  cloth  is  tacked  completely,  great  care  should  be  taken  to  see  that 
the  paper  drawing  is  so  placed  that  all  horizontal  lines  are  truly  horizontal 
in  order  that  the  T-square  may  be  used  to  the  best  advantage.     If  the 
drawing  paper  is  too  small  to  be  held  by  the  same  tacks,  it  should  be 
fastened  before  the  cloth  is  put  on.     Two  tacks  are  usually  sufficient  for 
this  purpose  and  if  put  at  the  upper  corners  will  seldom  be  in  the  way  of 
the  T-square.     It  may  be  desirable  to  use  small  upholsterers'  tacks, 
driven  with  a  hammer,  to  fasten  the  drawing  paper  to  the  board,  for  they 
will  not  interfere  with  the  instruments  during  the  making  of  the  drawing 
or  of  the  tracing.     Some  draftsmen  prefer  to  use  these  tacks  for  holding 
the  tracing  cloth  in  place  also,  particularly  when  the  T-square  or  the  tri- 
angles must  be  used  near  the  corners;  but  if  the  cloth  needs  to  be  re- 
stretched  very  frequently  the  use  of  such  tacks  is  hardly  practical. 

2.  Before  beginning  to  trace,  the  draftsman  should  make  sure  that  the 
surface  of  the  cloth  is  in  condition  to  receive  the  ink  properly.     This 
may  be  ascertained  by  trial  on  a  small  piece  of  the  same  cloth,  upon  the 
margin  of  the  sheet  which  will  be  subsequently  trimmed  off,  or  even  upon 
one  of  the  lines  of  the  drawing  itself.     Some  of  the  better  grades  of  tracing 
cloth  will  often  "take  "  ink  without  treatment,  and  it  is  preferable  to  use 
it  that  way.     More  frequently  the  surface  of  the  cloth  is  slightly  oily 
and  the  lines  appear  ragged.     The  common  method  of  overcoming  this 
disadvantage  is  to  sprinkle  upon  the  cloth  powdered  chalk  or  pumice 
stone,  specially  prepared  tracing  cloth  powder,  or  even  talcum  powder, 
and  to  rub  it  in  with  a  clean  cloth.     After  a  thorough  rubbing  has  spread 
the  powder  over  the  whole  surface,  another  clean  cloth,  or  a  brush,  should 


be  used  to  remove  completely  all  the  excess  powder  to  prevent  the  clog- 
ging of  the  pen.  If  too  much  powder  remains,  much  of  the  ink  falls  upon 
it  rather  than  upon  the  cloth,  and  the  lines  easily  wear  away.  Further- 
more, when  too  much  powder  is  used,  the  eraser  soon  becomes  clogged  and 
is  made  less  effective.  Accordingly,  it  is  often  preferable  to  "  surface  "  the 
cloth  by  means  of  a  sponge  eraser,  rubbing  the  grease  off  instead  of  cover- 
ing it  or  absorbing  it  with  the  powder.  This  is  particularly  true  when  the 
effects  of  the  oil  are  not  very  apparent,  for  the  cloth  is  thus  rendered  much 
more  satisfactory  to  work  upon.  The  surface  of  the  cloth  should  be  kept 
clean,  and  the  path  of  the  pen  cleared  of  all  lint,  dust,  and  pieces  of  eraser. 
A  brush  should  be  constantly  available  for  this  purpose,  but  care  should 
be  taken  that  all  ink  on  the  drawing  is  dry  before  the  brush  is  used. 

3.  The  draftsman's  equipment  should  include  a  good  ruling  pen,*  and 
he  should  not  only  be  familiar  with  its  use,  but  also  be  able  to  keep  it  in 
good  working  order.  When  not  in  use  the  pen  should  be  left  with  the 
nibs  separated  in  order  to  relieve  the  springs. 

The  ruling  pen  should  be  held  between  the  thumb  and  forefinger,  resting  against  the 
middle  finger  to  hold  it  firmly.  The  adjusting  screw  should  be  held  away  from  the 
draftsman  so  that  it  may  be  readily  turned  with  the  middle  finger  to  change  the  setting. 
The  nibs  should  be  parallel  to  the  straight-edge,  and  the  handle  should  be  slightly 
inclined,  with  the  top  in  advance  as  drawn  from  left  to  right.  The  handle  should  re- 
main in  a  plane  through  the  line  to  be  drawn,  the  plane  being  nearly  perpendicular  to 
the  plane  of  the  drawing.  See  page  58:6.  The  pen  should  never  be  pushed  back- 
ward, even  for  a  short  distance,  but  should  always  be  literally  "drawn." 

It  is  important  to  keep  the  pen  clean.  The  pen  should  not  be  filled 
until  the  draftsman  is  ready  to  use  it,  and  it  should  be  used  practically 
continuously  while  it  contains  ink.  Even  when  interrupted  from  work 
the  draftsman  should  take  time  to  wipe  his  pen  before  laying  it  down. 
This  can  be  quickly  done  if  a  large  cloth  is  kept  hanging  near  the  left- 
hand  corner  of  the  board  or  in  some  other  convenient  place. 

Old  tracing  cloth,  thoroughly  washed  with  soap  and  water,  makes  an  ideal  pen  wiper. 
The  wipers  which  are  furnished  with  bottles  of  ink  are  too  small  to  be  serviceable.  A 
pen  wiper  should  be  free  from  lint. 

*  For  more  complete  treatises  on  drawing  instruments  and  their  use  see  Blessing 
and  Darling's  "  Elements  of  Drawing,"  John  Wiley  and  Sons,  Inc.,  New  York;  French  'a 
"Engineering  Drawing,"  McGraw-Hill  Book  Co.,  Inc.,  New  York;  or  Kirby's  "The 
Fundamentals  of  Mechanical  Drawing,"  John  Wiley  and  Sons,  Inc.,  New  York. 


CHAPTER  X 


INKING  AND  TRACING 


57 


If  ink  is  permitted  to  dry  in  the  pen  it  should  be  removed  before  the  pen  is  used  again. 
If  allowed  to  remain  it  will  cause  the  pen  to  corrode;  this  will  not  only  make  it  more 
difficult  to  keep  clean,  but  will  eventually  prevent  precise  work.  Dried  ink  should 
never  be  removed  from  a  pen  with  a  knife  or  scratcher  for  the  inner  surfaces  will  become 
so  roughened  that  the  ink  will  not  feed  properly.  Furthermore,  a  much  simpler  and 
more  effective  method  is  to  dip  the  pen  in  red  ink,  which  will  dissolve  the  caked  ink 
so  that  it  may  be  wiped  off.  To  avoid  all  of  this,  the  draftsman  should  form  the  habit 
of  always  wiping  his  pen  before  laying  it  aside  even  momentarily,  while  the  ink  is  still 
liquid;  it  takes  only  a  moment  for  the  ink  to  dry  enough  to  clog  the  pen,  and  after 
this  happens  it  is  usually  a  waste  of  time  to  attempt  to  use  the  pen  again  without 
refilling  it. 

The  ink  should  flow  as  soon  as  the  pen  touches  the  cloth.  In  case  the  pen  has  been 
left  unused  only  for  a  moment  and  the  ink  has  dried  slightly  in  the  extreme  point,  the 
flow  may  often  be  started  without  refilling  the  pen  by  making  a  few  short  strokes  on  a 
piece  of  paper,  wood,  or  cloth.  It  is  a  good  plan  to  wipe  occasionally  the  side  of  the 
pen  which  bears  against  the  straight-edge,  for  this  not  only  keeps  the  ink  flowing  well, 
but  prevents,  in  large  measure,  the  ink  from  running  under  the  straight-edge.  If, 
when  the  pen  is  adjusted  for  fine  lines  the  ink  cannot  be  started  by  the  expedients 
just  mentioned,  the  nibs  may  be  separated  temporarily  until  a  heavy  line  can  be 
drawn,  and  then  readjusted  to  give  the  desired  width. 

The  ruling  pen  is  usually  filled  by  means  of  the  quill  in  the  cork  of  the  ink  bottle. 
When  used  immediately  after  a  lettering  pen  or  other  pen  in  which  considerable  ink  is 
left,  the  ink  may  be  transferred  from  one  pen  to  the  other;  this  saves  ink  and  often  time, 
and'prolongs  the  life  of  the  pen  wiper.  Similarly,  ink  may  be  restored  to  the  bottle  by 
touching  the  pen  to  the  quill.  Care  should  be  taken  to  avoid  getting  any  ink  on  any 
part  of  the  pen  other  than  between  the  nibs,  particularly  on  the  part  that  bears  against 
the  straight-edge.  The  pen  while  being  filled  should  never  be  held  over  a  drawing. 

It  is  important  not  to  get  too  much  ink  in  the  pen,  particularly  for  fine-line  work. 
It  is  difficult  to  retain  a  constant  width  of  line  if  the  amount  of  ink  in  the  pen  is  greatly 
increased;  it  is  better  to  increase  the  amount  slightly  before  the  pen  is  entirely  empty. 
Experience  will  show  the  proper  amount  to  use  in  pens  of  different  shape  under  different 
conditions.  For  short  fine  lines  the  depth  of  ink  above  the  points  should  seldom 
exceed  ^  or  J  of  an  inch. 

1.  If  a  pen  is  not  working  well,  a  draftsman  should  be  able  to  fix  the 
points  so  that  a  clear-cut  even  line  of  any  width  from  the  finest  to  the 
coarsest  can  be  drawn.  If  the  points  are  too  dull  it  is  impossible  to  draw 
fine  lines  satisfactorily,  and  if  the  points  are  of  uneven  length  one  edge 
or  the  other  of  a  coarse  line  will  be  ragged.  If  a  pen  is  in  good  condition, 
it  should  be  possible  to  draw  lines  at  different  speeds  without  having 
them  vary  in  width,  or  to  stop  the  pen  completely  and  start  it  again  with- 
out leaving  a  pool  or  other  evidence  of  having  stopped  it. 


To  sharpen  a  pen,  rub  the  outside  surface  first  of  one  nib  and  then  of  the  other  on  a 
fine  oil  stone.  In  order  to  keep  the  outside  surface  of  a  nib  curved,  the  pen  should  be 
moved  in  the  form  of  a  figure  eight,  with  a  slight  rocking  motion,  so  that  the  whole 
edge  of  the  nib  is  sharpened  uniformly.  Care  should  be  taken  to  avoid  making  flat 
spots,  or  sharpening  one  nib  more  than  the  other.  After  both  are  sharpened  so  that 
the  edges  show  no  shiny  worn  places,  make  the  two  nibs  of  the  proper  relative  length 
by  drawing  the  pen  lightly  along  the  stone,  holding  it  in  the  same  plane  as  when  draw- 
ing a  line,  i.e.,  approximately  normal  to  the  stone,  but  swinging  the  handle  in  this 
plane  to  give  a  curved  edge.  Test  the  lengths  of  the  nibs  by  drawing  several  heavy 
lines  of  different  widths.  If  a  line  appears  ragged  on  one  side,  the  nibs  do  not  bear 
evenly,  or  else  one  nib  is  too  dull.  If  the  pen  will  draw  heavy  lines  well,  test  it  for 
fine  lines.  The  nibs  may  have  been  dulled  slightly  in  the  process  of  evening  their 
lengths;  if  so  they  should  be  re-sharpened.  If  reasonable  precautions  are  taken  to 
avoid  excessive  grinding  the  draftsman  should  be  able  to  obtain  edges  at  the  first  trial 
which  are  even  and  yet  of  the  right  sharpness.  The  pen  should  not  be  left  too  sharp, 
for  it  will  either  cut  the  cloth  or  else  make  such  a  deep  impression  that  it  is  difficult  to 
erase  a  line  when  occasion  arises. 

2.  The  legs  of  the  compasses  should  be  bent  at  the  knuckle  joints 
until  the  pen  and  the  arm  which  carries  the  pivot  point  are  both  perpen- 
dicular to  the  plane  of  the  cloth.     The  compasses  should  be  set  to  the 
proper  radius  by  placing  the  pivot  point  at  the  center  of  the  arc  and 
moving  the  pen  until  it  is  immediately  above  the  line  to  be  inked,  close 
to  the  drawing  but  not  in  contact  with  it.     In  drawing  a  curve  the  com- 
passes should  be  inclined  so  that  the  top  of  the  pen  is  slightly  in  advance 
of  the  point.     A  curve  should  be  drawn  with  a  continuous  motion,  and  a 
complete  circle  should  be  closed  by  carrying  the  pen  a  little  past  the  be- 
ginning.    The  weight  of  the  pen  is  sufficient  to  insure  a  good  line  without 
additional  pressure,  and  care  should  be  taken  to  avoid  pressure  sufficient 
to  alter  the  radius  or  to  move  the  pivot  so  as  to  cause  a  crude  junction. 

3.  The  lettering  pen  should  be  well  adapted  to  the  individual  who  uses 
it,  with  a  pen-holder  of  suitable  size  so  that  the  hand  will  not  become 
cramped.     Some  draftsmen  obtain  excellent  results  with  fine  points 
while  others  cannot  use  them  without  spreading  the  nibs  so  as  to  make 
lines  of  uneven  width.     A  long  fine  stub  pen  will  usually  give  excellent 
results  for  most  letters  and  figures  of  a  structural  drawing  (page  47  :  5), 
a  fine  pen  being  provided  for  drawing  arrows  and  arrow  heads  or  special 
work  for  which  the  stub  is  too  coarse.     A  ball-pointed  pen  is  often  used 
for  titles  and  other  prominent  lettering.     Some  draftsmen  use  a  ruling 


58 


PART   II  —  STRUCTURAL  DRAFTING 


pen  for  a  lettering,  but  when  this  is  done  a  special  pen  should  be  kept  for 
the  purpose  for  it  cannot  be  kept  in  condition  for  ruling. 

1.  Two  bottles  of  best  quality  India  waterproof  black  ink  should  be 
used,  one  for  instrumental  work  and  the  other  for  lettering.     The  former 
should  have  a  quill  for  filling  the  ruling  pen,  but  the  latter  may  have  the 
quill  cut  off,  because  it  is  quicker  and  more  satisfactory  to  dip  the  letter- 
ing pen  into  the  bottle  than  to  use  the  quill.     The  bottle  with  the  quill 
should  be  kept  corked  except  during  the  actual  filling  of  the  pen,  but  the 
other  may  be  left  uncorked  as  long  as  the  lettering  pen  is  in  constant  use. 
This  would  not  be  feasible  if  only  one  bottle  of  ink  were  used;  so  much 
dust  collects  in  the  open  bottle,  and  so  much  ink  evaporates  leaving  a 
deposit,  that  the  ink  is  soon  unfit  for  use  in  drawing  pens,  though  it  may 
still  be  used  in  lettering  pens.     Each  new  bottle  of  ink  should  be  reserved 
for  instrumental  work,  the  remainder  of  the  ink  in  the  former  bottles 
being  combined  for  lettering.     Ink  should  never  be  diluted  with  water; 
if  it  becomes  too  thick  for  use  it  should  be  thrown  out  and  replaced. 

2.  If  red  ink  is  used,  a  quality  should  be  selected  which  can  be  erased. 
No  red  ink  can  be  erased  so  easily  as  black  ink,  but  some  red  inks  cannot 
be  removed  at  all.     It  should  be  waterproof;  otherwise  it  is  liable  to 
spread  when  stored  in  cool  vaults. 

3.  An  ink  bottle  should  never  be  shaken,  for  no  benefit  is  derived  and 
the  sediment  is  stirred  up  so  that  it  is  liable  to  get  into  the  pen.     Further- 
more, bubbles  are  formed  in  the  neck  of  the  bottle  which  draw  the  ink 
from  the  quill,  <  so  that  it  is  difficult  to  obtain  enough  to  fill  the  pen. 

4.  Frozen  ink  is  useless  and  it  is  usually  unsatisfactory  when  thawed. 
The  bottles  should  be  kept  away  from  windows  in  extremely  cold  weather 
to  prevent  the  ink  from  freezing. 

5.  The  straight-edge  should  be  placed  between  the  draftsman  and  the 
line  to  be  inked,  so  that  the  near  side  of  the  pen  bears  upon  the  far  side 
of  the  straight-edge.     Care  should  be  taken  to  keep  the  pen  against  the 
straight-edge,  but  to  exert  no  more  pressure  than  necessary  to  insure 
this.     The  pressure  should  be  constant,  for  otherwise  the  width  of  a  line 
will  be  reduced  as  the  nibs  of  the  pen  are  pressed  together.     The  pressure 
of  the  pen  upon  the  cloth  or  paper  depends  upon  the  sharpness  of  the  pen 
and  the  quality  of  the  surface,  but  it  should  never  be  greater  than  neces- 
sary to  insure  an  even  line. 


6.  The  draftsman  shquld  not  attempt  to  draw  too  close  to  the  straight- 
edge, lest  the  ink  run  under  and  blot.     This  distance  depends  somewhat 
upon  the  shape  of  the  pen  and  the  thickness  of  the  straight-edge,  but 
after  a  little  practice  the  draftsman  will  learn  how  close  he  can  work  to 
the  best  advantage.     One-fiftieth  of  an  inch  may  be  taken  as  a  guide  to 
the  beginner;  this  corresponds  very  closely  to  the  smallest  division  (J") 
on  the  scale  of  1"  =  1'.     After  inking  a  line  one  should  never  attempt 
to  pick  up  the  straight-edge  until  it  has  been  moved  a  safe  distance  away 
from  the  line,  i.e.,  toward  the  draftsman.     Otherwise  it  is  difficult  to  pick 
it  up  without  letting  it  slip  into  the  wet  ink  and  cause  a  serious  blot. 

7.  An  easy  posture  should  always  be  assumed  before  a  line  is  drawn, 
for  it  is  difficult  to  do  good  work  in  a  cramped  position.     The  drawing 
board  may  sometimes  be  turned  to  advantage.     Lines  should  be  drawn 
with  a  full  arm  motion,  with  the  third  and  fourth  fingers  resting  lightly 
upon  the  straight-edge  as  a  guide  to  give  better  control.     The  elbow 
should  not  be  rested  upon  the  drawing.     Near  the  end  of  the  line  the 
guiding  fingers  should  be  stopped  just  before  the  fingers  which  hold  the 
pen,  to  facilitate  stopping  the  pen  at  the  exact  point.     This  may  be  done 
in  such  a  manner  that  the  motion  of  the  pen  will  not  be  interrupted. 
Very  short  lines  may  be  drawn  with  this  finger  motion  alone. 

8.  Each  full  line  should  be  drawn  with  a  continuous  stroke.     It  is 
important  to  have  sufficient  ink  in  the  pen  to  complete  the  line.     If  it  is 
discovered  that  the  ink  will  give  out  before  the  end  of  the  line  is  reached, 
it  is  best  to  stop  abruptly,  preferably  at  some  intersection,  and  to  begin 
at  the  same  point  after  refilling  the  pen.     If  the  ink  runs  out  before  the 
draftsman  is  aware  of  its  being  low,  the  ragged  part  of  the  line  should  be 
retraced  after  the  pen  is  refilled.     In  this  event  it  is  important  to  try  the 
pen  on  a  separate  sheet  to  make  sure  that  the  line  is  of  the  proper  width 
before  applying  it  to  the  drawing,  for  a  pen  is  likely  to  make  a  wider  line 
after  being  cleaned  and  refilled  than  when  nearly  empty. 

9.  It  is  well  to  draw  all  lines  which  are  of  the  same  width  at  one  setting 
of  the  pen,  if  possible,  in  order  to  gain  uniformity.     Even  the  pens 
which  are  made  so  that  they  may  be  opened  and  cleaned  without  chang- 
ing the  setting  do  not  always  make  lines  of  the  same  width  before  and 
after  cleaning.     In  order  to  produce  a  more  constant  flow,  the  pen  should 
be  refilled  before  it  is  entirely  empty. 


CHAPTER  X 


INKING  AND  TRACING 


59 


1.  Care  should  be  taken  to  stop  the  pen  at  the  exact  end  of  each  line 
in  order  to  give  a  finished  appearance  to  the  drawing.     The  pen  should 
be  lifted  immediately,  when  the  end  is  reached,  to  prevent  the  ink  from 
running  out  and  forming  a  pool,  which  it  is  liable  to  do,  particularly 
when  the  pen  and  the  cloth  are  not  both  in  perfect  condition.     The  pen 
should  always  be  lifted  vertically  to  avoid  a  false  mark. 

2.  Lines  should  be  drawn  away  from  intersections,  as  far  as  possible, 
rather  than  toward  them,  particularly  when  several  lines  meet  in  a  com- 
mon point.     A  line  should  never  be  drawn  to  meet  another  line  until  the 
latter  is  perfectly  dry. 

3.  Heavy  lines  which  represent  web  sections  (page  37:2)  and  other 
lines  which  are  wider  than  the  main  lines  or  the  border  lines  of  a  drawing 
should  each  be  made  of  two  or  more  component  parts,  i.e.,  part  of  the 
width  should  be  drawn  and  allowed  to  dry,  then  another  part,  and  so  on 
until  the  full  width  is  completed.     If  the  full  width  is  drawn  with  one 
stroke  or  setting  of  the  pen,  the  ink  will  flow  so  freely  that  it  will  take  too 
long  to  dry,  will  pucker  the  cloth,  and  will  make  it  impossible  to  get  clean 
intersections  because  the  ink  will  form  a  pool  where  two  lines  meet.     If 
three  lines  are  used  for  building  up  a  heavy  line,  the  first  two  are  drawn 
to  form  the  boundaries  of  the  required  line,  and  they  should  be  so  drawn 
that  they  are  parallel  and  entirely  within  the  desired  width.     After  these 
two  component  parts  are  dry,  the  third  line  may  be  drawn  to  fill  in  the 
space  between  them.     It  should  not  be  necessary  to  use  more  than  three 
lines  and  usually  two  will  suffice.     Border  lines  are  generally  not  so  wide 
that  they  cannot  be  drawn  with  a  single  stroke,  but  often  two  strokes 
will  give  better  results. 

4.  In  the  inking  of  several  parallel  lines,  the  triangles  or  T-square 
should  be  used  in  the  same  manner  as  in  the  penciling  of  the  lines  to  in- 
sure their  being  parallel.     If  only  a  single  triangle  is  used  in  the  attempt 
to  ink  over  the  pencil  lines,  a  slight  variation  usually  results,  which  is 
quite  apparent.     For  methods  of  drawing  many  parallel  lines  equidistant, 
as  in  cross  section  lining,  see  page  37 : 2. 

5.  All  curves  should  be  inked  before  the  straight  lines  which  are  tan- 
gent to  them.     A  straight  line  is  tangent  to  a  curved  line  when  the  center 
of  the  one  is  tangent  to  the  center  of  the  other,  the  width  at  the  point  of 
tangency  being  no  greater  than  the  width  of  either  line  at  any  other  point. 


If  the  straight  line  is  narrower  than  the  curved  line,  as  for  example  the 
projection  line  for  a  dimension  to  the  extreme  outside  of  a  curved  surface, 
the  outer  edges  should  be  tangent  instead  of  the  centers. 

6.  At  practically  no  time  should  it  be  necessary  to  wait  for  ink  to  dry. 
It  does  not  require  much  ingenuity  to  find  something  to  do  on  one  part 
of  the  drawing  while  the  ink  is  drying  on  another  part.     The  man  who 
idly  fans  the  ink  with  a  triangle  not  only  wastes  valuable  time,  but  at- 
tracts the  attention  of  others  to  the  fact  that  he  is  not  at  work. 

7.  On  rush  work  of  revision,  or  other  work  which  is  confined  to  a  small 
part  of  the  drawing,  it  may  be  desirable  to  ink  in  the  vicinity  of  wet  lines. 
This  may  be  done  by  placing  a  triangle  on  each  side  of  the  wet  lines,  and 
then  laying  across  these  two  triangles  a  third  triangle  to  be  used  as  a 
straight-edge.     This  cannot  blur  the  wet  lines  since  the  straight-edge  is 
elevated  above  the  surface  of  the  cloth  in  such  a  way  that  it  cannot  touch 
the  lines.     For  a  small  area  it  may  be  sufficient  to  lay  one  triangle  across 
the  central  opening  of  a  large  triangle.     Care  should  be  taken  not  to 
draw  a  line  which  will  intersect  a  wet  line  or  figure. 

8.  A  blotter  should  never  be  laid  upon  wet  drawing  ink  to  hasten  dry- 
ing.    In  fact  the  blotter  should  never  be  used  on  a  drawing  except  to 
absorb  superfluous  ink  from  a  blot  or  from  a  line  to  be  erased,  and  then 
only  by  touching  its  corner  to  the  crest  of  the  pool,  without  touching  the 
cloth.     If  the  blotter  touches  the  cloth  when  wet,  it  makes  the  ink  pene- 
trate so  deeply  that  it  is  difficult  to  erase  it,  in  fact  more  difficult  than  if 
it  were  allowed  to  dry  without  the  use  of  a  blotter. 

9.  In  order  to  obtain  the  best  results  in  inking  or  tracing,  a  systematic 
method  of  procedure  should  be  followed.     The  tracing  should  not  be 
started  until  the  penciled  drawing  is  complete,  especially  if  the  tracing  is 
made  by  a  person  other  than  the  one  who  makes  the  drawing.     In  case 
the  drawing  and  the  tracing  are  done  by  the  same  draftsman,  he  should 
either  make  the  penciled  drawing  complete,  or  else  work  directly  upon 
the  tracing  cloth,  as  explained  in  Chapter  XII,  page  65.     The  only 
modification  of  this  rule  is  noted  on  page  66: 1.     The  order  of  procedure 
given  in  the  following  paragraphs  is  recommended. 

10.  All  the  lines  of  a  drawing  should  be  inked  before  any  of  the  figures 
or  notes.  For  widths  of  lines,  see  page  37: 1.  Ordinarily  it  is  best  to 
ink  all  the  lines  which  are  of  one  width  before  changing  the  setting  of  the 


60 


PART   II  —  STRUCTURAL  DRAFTING 


pen  for  another  width  (page  58:9);  but  if  the  work  is  to  be  interrupted 
for  a  considerable  length  of  time  so  that  atmospheric  changes  might  cause 
the  cloth  to  expand  or  contract  it  may  seem  better  to  confine  the  inking 
to  one  view,  or  to  so  much  of  the  drawing  as  can  be  completed  before  the 
interruption,  especially  if  the  drawing  is  complicated  and  the  number  of 
intersecting  lines  is  large. 

1.  All  fine  line  curves  should  be  inked  first,  and  then  the  rest  of  the 
fine  lines,  including  the  dimension  lines,  and  the  center  lines,  but  not 
including  cross  section  lines,  or  fine  lines  which  are  tangent  to  heavy  line 
curves.     The  horizontal  lines  should  be  drawn  first,  beginning  at  the  top 
and  working  down  the  sheet  to  save  waiting  for  the  ink  to  dry;  next  the 
vertical  lines,  beginning  at  the  left  and  working  toward  the  right;  and 
then  all  other  lines  of  the  same  width,  working  in  some  systematic  order 
to  prevent  the  omission  of  any. 

2.  The  heavier  main  lines  of  the  drawing  should  be  inked  next,  follow- 
ing the  same  order  as  given  for  the  lighter  lines  in  the  preceding  paragraph. 

3.  The  rivets  and  holes  may  be  put  in  next.     These  should  never  be 
drawn  until  the  lines  are  drawn,  for  it  is  simpler  and  more  satisfactory 
to  center  the  rivets  on  a  line  than  it  is  to  draw  a  line  through  the  centers 
of  a  row  of  rivets.     The  rivets  should  always  be  drawn  approximately  to 
scale  with  a  bow-pen  or  a  riveter. 

Few  bow-pens  can  be  adjusted  to  make  circles  small  enough  for  the  general  require- 
ments of  structural  drafting,  and  riveters  are  much  better  adapted  to  the  purpose. 
The  riveters  fitted  for  ink  only,  i.e.,  riveting  pens,  are  recommended  instead  of  those 
which  are  interchangeable  for  ink  and  for  pencil.  A  fixed  needle  point  is  held  verti- 
cally while  the  revolving  pen  is  twirled  around  it.  The  pen  can  be  set  to  make  a 
circle  which  is  so  small  that  it  is  virtually  a  period,  and  can  be  lifted  out  of  the  way 
while  the  needle  point  is  being  centered.  Such  a  riveter  should  form  part  of  the  equip- 
ment of  every  structural  draftsman. 

The  appearance  of  any  drawing  is  marred  by  freehand  rivets  and  holes. 
For  the  conventional  method  of  indicating  rivets  and  holes,  and  for  the 
sizes  of  the  circles,  see  page  40: 6.  All  shop  rivets  of  the  same  diameter 
should  be  drawn  with  one  setting  of  the  riveting  pen  in  order  to  make 
them  of  uniform  size,  and  the  same  precaution  should  be  observed  in 
drawing  the  holes  for  the  field  rivets.  The  latter  may  be  filled  in  solid 
at  once,  but  considerable  time  is  required  for  the  little  puddles  to  dry  so 


that  they  will  not  smear,  and  for  this  reason  it  may  save  delay  to  wait 
until  the  rest  of  the  drawing  is  completed  before  filling  in  the  holes  or 
else  to  fill  them  in  a  few  at  a  time  while  dimensioning.  Some  draftsmen 
prefer  to  draw  all  arrow  heads  before  putting  any  of  the  dimension  figures 
on  the  drawing;  in  this  case  the  open  holes  may  be  filled  in  at  the  same 
time.  See  page  47  :  4  for  the  styles  of  arrow  heads.  When  filling  the 
circles  for  the  field  rivets  it  is  an  excellent  plan  to  slip  a  blotter  under  the 
cloth  to  absorb  any  ink  that  may  run  through  the  holes  made  by  the 
needle  point  of  the  bow-pen  or  the  riveter.  By  using  a  little  forethought 
the  draftsman  can  usually  plan  his  work  so  that  the  ink  will  be  dry  on 
part  of  the  drawing  by  the  time  that  he  completes  the  holes  and  arrow 
heads  on  the  rest,  so  that  he  can  proceed  at  once  with  the  dimensions. 

4.  After  the  arrow  heads  have  been  inked,  the  dimension  figures  may 
be  put  on,  but  this  should  be  done  systematically  in  order  that  none  will 
be  omitted.     On  some  drawings  it  may  be  well  to  ink  them  in  the  order 
of  importance,  and  on  others  in  the  order  in  which  the  shopmen  will  use 
them,  thus  making  sure  that  sufficient  dimensions  are  given.     If  the 
penciled  drawing  is  well  made,  however,  the  dimensions  on  one  view  may 
be  inked  first,  one  line  of  dimensions  at  a  time,  and  then  the  dimensions 
on  the  next  view,  and  so  on.     When  a  detail  is  dimensioned  chiefly  in  one 
view,  but  has  a  gage  or  a  few  similar  figures  in  another  view,  it  is  well  to 
ink  these  figures  in  connection  with  the  rest  of  the  detail,  rather  than  to 
wait  until  the  remainder  of  the  view  is  inked. 

5.  After  the  drawing  has  been  dimensioned,  all  material  should  be 
billed  as  outlined  in  Chapter  VII,  page  43;  then  the  list  of  members 
required  and  all  notes  should  be  inked,  first  the  specific  notes  on  various 
parts  of  the  drawing,  then  the  general  notes,  as  outlined  in  Chapter  IX, 
page  52.     For  all  of  this  work  pencil  guide  lines  should  be  used,  not 
merely  by  beginners,  as  students  are  wont  to  believe,  but  by  experienced 
draftsmen  as  well.     Guide  lines  are  essential  to  all  good  lettering;  like 
the  carpenter's  staging,  they  are  used  by  the  best  men  as  well  as  by  the 
novices,  but,  like  the  carpenter's  staging,  they  should  be  removed  after 
the  work  has  been  completed.     To  obviate  the  necessity  of  ruling  and 
erasing  lines  on  each  drawing,  a  small  sheet  ruled  once  for  all  with  parallel 
lines  at  proper  distances  apart,  may  be  slipped  under  the  tracing  cloth 
where  the  lettering  is  to  be,  and  used  instead  of  the  pencil  guide  lines. 


CHAPTER  X 


INKING  AND  TRACING 


*61 


is  convenient  to  have  a  large  number  of  parallel  lines  on  this  sheet  not 
only  to  provide  for  notes  which  have  many  lines,  but  also  to  simplify  the 
placing  of  the  sheet  in  the  desired  position.  Diagonal  red  lines  drawn 
at  the  standard  slope  for  inclined  letters  are  of  great  assistance  in  main- 
taining a  uniform  slant  in  lettering.  A  convenient  size  for  this  sheet  is 
5"  X  8";  if  smaller  it  is  difficult  to  place  it  under  the  cloth  in  the  right 
position.  Sheets  with  different  spacing  may  be  made  for  various  sizes  of 
letters,  or  different  spaces  may  be  combined  on  one  sheet,  if  the  change 
from  one  to  the  other  is  made  conspicuous.  Uniform  spaces  of  TV  make 
good  units,  for  a  single  space  may  be  used  for  small  notes,  two  spaces  for 
Required  Lists,  and  three  spaces  for  titles.  Simple  freehand  letters 
should  be  used  entirely,  and  the  draftsman  should  practice  lettering  until 
proficient,  for  a  good  looking  drawing  may  be  easily  marred  by  crude 
lettering.*  Slanting  letters  are  preferable  to  vertical  letters  because 
*  The  beginner  should  obtain  some  standard  book  on  lettering,  such  as  Reinhardt's 


deviations  from  a  uniform  slope  are  less  apparent  than  deviations  from 
the  vertical.  Most  draftsmen  can  letter  more  rapidly  with  sloping  letters 
than  with  vertical  letters. 

1.  Finally  the  title  should  be  traced  and  the  border  inked.     For  sug- 
gestions for  making  the  title  and  the  border  see  page  54  : 1-7. 

2.  As  soon  as  the  tracing  is  removed  from  the  board  it  should  be  in- 
verted so  that  the  draftsman  may  ascertain  if  any  ink  has  passed  through 
defects  in  the  cloth,  or  through  holes  made  by  the  instruments.     All  such 
blots  should  be  removed,  for  they  would  cause  spots  on  the  prints  and 
thereby  mar  the  appearance  just  as  if  on  the  face  of  the  tracing;  they 
might  cause  serious  trouble  if  an  important  figure  was  thus  altered  or 
obliterated. 

"Lettering  for  Draftsmen,  Engineers  and  Students,"  D.  Van  Nostrand  Co.,  New 
York;  Blessing  and  Darling's  "Elements  of  -Drawing,"  John  Wiley  and  Sons,  Inc., 
New  York,  or  French's  "Engineering  Drawing,"  McGraw-Hill  Book  Co.,  Inc.,  New  York. 


CHAPTER  XI 
ERASING 

SYNOPSIS:  It  frequently  happens  that  parts  of  structural  drawings  must  be  removed 
on  account  of  mistakes  or  changes.  Every  draftsman  should  learn  to  erase  in  such  a 
manner  as  to  leave  the  least  possible  evidence  of  erasure,  even  when  several  erasures 
are  made  in  the  same  place  on  a  drawing. 


1.  To  erase  any  part  of  a  drawing  properly  is  just  as  important  as  to 
ink  or  trace  properly,  and  the  draftsman  should  expect  to  devote  a  con- 
siderable part  of  his  time  to  painstaking  and  careful  erasing.     In  the 
first  place,  he  must  correct  his  own  mistakes  and  errors  of  judgment,  and 
in  the  second  place,  he  must  frequently  make  changes  which  may  be  due 
either  to  mistakes  of  others  or  to  changes  in  design.     Many  good  looking 
drawings  are  practically  ruined  by  careless  erasing. 

2.  The  object  of  erasing  is  not  merely  to  remove  part  of  a  drawing, 
but  to  remove  it  in  such  a  manner  that  other  lines  and  figures  may  be 
placed  in  the  same  spot  without  having  the  change  apparent  on  the  blue- 
print.    This  can  be  accomplished  only  by  a  person  who  fully  realizes  the 
difficulty,  and  who  exercises  great  care  and  patience. 

3.  Erase  Willingly.  —  The  first  and  often  the  only  indication  of  friction 
between  a  beginner  and  his  superiors  usually  arises  because  he  objects  to 
erasing.     While  he  should  never  make  changes  until  he  approves  them, 
yet  he  should  stand  in  readiness  to  believe  that  the  more  experienced 
checker  has  good  reasons  for  most  changes  and  he  should  try  to  see  his 
point  of  view;  moreover,  the  objections  of  the  novice  are  more  likely  to 
be  heeded,  if,  instead  of  attempting  to  convince  the  checker  that  minor 
changes  should  not  be  made  because  they  involve  too  much  erasing,  he 
reserves  his  arguments  for  more  important  matters.     The  friction  should 
be  between  the  draftsman  and  the  drawing  not  between  the  draftsman 
and  the  checker.     To  argue  over  erasing  is  usually  futile,  and  more  time 
is  lost  than  would  be  used  in  making  the  corrections  at  once;  furthermore, 


62 


the  draftsman  is  liable  to  lower  himself  in  the  estimation  of  the  checker. 
He  should  be  more  tactful. 

4.  The  draftsman  should  profit  by  the  criticisms  of  the  checker,  and 
guard  against  mistakes  similar  to  those  which  have  been  corrected  on 
former  drawings.    Erasing  mistakes  will  often  help  him  to  remember  them. 
A  new  man  is  judged  not  so  much  by  the  mistakes  he  makes,  as  by  the 
mistakes  he  makes  a  second  time;  if  he  is  careful  not  to  repeat  any  mistake 
it  will  not  be  long  before  he  will  outrank  the  men  who  are  not  so  careful. 

5.  Ink  should  be  removed  from  tracing  cloth  by  means  of  an  eraser. 
The  secret  of  erasing  on  cloth  is  to  rub  so  lightly  and  slowly  and  with  such 
frequent  rests,  that  the  cloth  will  not  become  noticeably  heated ;  if  it  be- 
comes a  bit  warm  the  preparation  which  makes  the  cloth  transparent 
will  become  softened  so  that  the  eraser  will  remove  it.     If  this  prepara- 
tion is  once  removed  the  cloth  is  made  opaque  so  that  a  white  spot  will 
show  on  the  blue  print,  and  the  surface  cannot  be  restored  for  further 
inking.     A  little  experience  will  show  how  many  strokes  may  be  made 
without  heating  the  cloth,  the  temperature  of  which  may  be  tested  with 
a  dry  finger.     When  there  are  several  different  parts  to  erase,  the  drafts- 
man can  rub  a  few  strokes  in  one  place,  then  in  another,  and  so  on,  until 
enough  time  has  elapsed  to  allow  the  first  part  to  become  entirely  cool, 
when  the  process  may  be  repeated.     The  cloth  should  be  supported  by  a 
smooth  hard  surface  before  the  eraser  is  applied;  unless  the  drawing 
board  is  unusually  free  from  holes  and  dents,  a  triangle  or  something 
similar  should  be  placed  under  the  part  to  be  erased. 


CHAPTER  XI 


ERASING 


63 


1.  The  Eraser.  —  Either  an  "ink  eraser  "  or  a  "pencil  eraser  "  may 
be  used  for  removing  ink  from  tracing  cloth.     The  former  is  more  effective 
but  it  is  liable  to  scratch  or  injure  the  cloth.     One  may  obtain  more  satis- 
factory results  with  a  pencil  eraser  if  one  has  abundant  patience  and 
avoids  excessive  speed  so  that  the  cloth  never  becomes  heated.     When 
the  ink  is  quite  thick  part  of  it  may  be  removed  with  an  ink  eraser  and 
the  remainder  with  a  pencil  eraser.     Whenever  an  ink  eraser  is  used  it 
should  be  followed  by  the  use  of  a  pencil  eraser  to  clean  the  drawing 
properly.     The  center  of  contact  should  be  kept  on  the  ink  to  be  re- 
moved lest  the  adjacent  cloth  become  seriously  damaged  before  the 
fact  is  realized.     An  eraser  will  often  become  soiled  or  clogged  from  use, 
particularly  when  used  on  heavy  lines  or  on  smooth  paper.     It  should 
be  cleaned  by  being  rubbed  on  clean  rough  paper  or  on  a  clean  portion 
of  the  drawing  board  reserved  for  the  purpose.     The  white  or  "ruby  " 
erasers  are  firmer  and  better  adapted  to  the  removal  of  ink  than  the 
"emerald  "  ones;  they  are  also  more  likely  to  be  self-cleaning. 

2.  A  special  ink  eradicator  for  tracing  cloth  is  on  the  market  but  it 
should  not  be  used  too  generally.       It  should  not  be  used  for  small 
erasures,  since  it  cannot  be  confined  to  small  area  to  good  advantage  and 
it  should  never  be  used  if  any  erasures  or  scratches  have  been  made  pre- 
viously within  the  same  area.     For  taking  out  a  whole  detail  or  other 
large  portion  of  a  drawing  the  liquid  eradicator  usually  proves  satisfac- 
tory. 

3.  A  knife  or  metal  scratcher  should  not  be  used  on  a  drawing  in 
place  of  an  eraser.     The  surface  of  the  cloth  is  so  damaged  that  it  is 
impossible  to  re-ink  properly  the  portion  which  has  been  scratched.     The 
cloth  often  becomes  so  opaque  where  a  knife  has  been  applied  that  the 
scratched  portion  shows  on  the  print  almost  as  distinctly  as  if  the  ink 
had  not  been  removed,  and  furthermore,  the  lines  appear  ragged.     A 
very  sharp  scratcher  in  the  hands  of  an  expert  can  be  used  sparingly  to 
advantage ;  but  as  a  rule,  the  use  of  a  knife  or  scratcher  is  a  confession  of 
laziness,  for  there  is  nothing  to  recommend  it  except  that  it  is  sometimes 
easier  to  scratch  out  a  small  section  of  a  line  than  it  is  to  erase  it  and  then 
have  to  replace  the  surrounding  lines  which  may  be  erased  also.     This 
advantage  is  offset  by  the  fact  that  drawings  frequently  have  to  be  re- 
traced when  a  later  revision  necessitates  inking  where  a  knife  has  been 


used.  Erasing  with  a  knife  nearly  always  involves  the  risk  of  injury  to 
the  cloth,  and  is  in  this  sense  a  dangerous  habit  which  is  not  j  ustified  by 
the  results;  better  results  are  almost  invariably  obtained  when  an  eraser 
is  used. 

4.  When  erasing  a  figure,  a  rivet,  or  small  detail,  which  is  close  to  other 
lines  or  figures,  one  may  use  an  erasing  shield  to  protect  the  surrounding 
parts,  and  thus  simplify  the  filling  in  afterwards. 

A  shield  may  be  made  by  cutting  any  desired  size  and  shape  of  aperture  through  a 
thin,  tough  card.  Erasing  shields  of  nickle-plated  brass  or  of  steel  may  be  bought, 
those  of  steel  being  recommended,  if  used  enough  to  keep  them  from  rusting,  because 
they  are  much  more  durable. 

5.  A  brush  should  be  used  to  remove  all  pieces  of  eraser  and  other 
foreign  matter  from  the  drawing  as  soon  as  the  desired  parts  have  been 
erased.     If  pieces  of  eraser  adhere  to  the  cloth  they  may  be  brushed  off 
more  easily  if  a  little  tracing  cloth  powder  (page  56  :  2)  is  sprinkled  over 
them. 

6.  The  surface  of  the  cloth  where  any  erasure  has  been  made  must  be 
treated  before  ink  is  applied,  or  the  ink  will  spread.     Although  chalk  or 
pumice  stone  are  frequently  used,  it  is  better  to  polish  the  cloth,  for 
the  new  lines  will  be  more  durable  if  on  the  cloth  itself,  than  if  partly 
on  the  powder.     A  triangle  or  other  hard  surface  should  be  slipped  under 
the  cloth,  and  a  smooth,  clean  piece  of  soapstone  or  celluloid  rubbed  over 
the  erased  area  until  the  cloth  shines.     Other  hard  surfaces  may  be  sub- 
stituted for  the  soapstone,  but  they  are  likely  to  soil  the  cloth.     An  end 
of  a  celluloid  triangle  serves  very  well  if  the  corners  are  rounded  and  used 
for  this  purpose  only,  care  being  taken  to  avoid  the  worn  part  when  the 
triangle  is  used  as  a  straight-edge. 

7.  After  erasures  have  been  made  and  the  cloth  has  been  polished,  all 
lines  and  figures  which  have  been  erased  by  mistake  should  be  replaced 
whether  there  is  anything  to  be  added  or  not.     This  point  is  frequently 
overlooked,  especially  if  only  a  small  portion  of  a  line  is  erased,  but  it 
requires  only  a  few  such  omissions  to  mar  the  appearance  of  a  drawing. 
In  order  to  prevent  blurring  or  blotting,  especially  if  the  erased  surface 
is  not  very  smooth,  the  heavier  lines  should  each  be  built  up  by  making 
several  fine  lines  until  the  desired  width  is  obtained,  no  line  being  drawn 
until  the  preceding  one  is  dry. 


64 


PART   II  —  STRUCTURAL  DRAFTING 


1.  If  pencil  lines  are  used  on  the  tracing  cloth,  they  may  be  left  until 
the  tracing  is  finished,  and  then  removed  along  with  any  accumulated 
dirt.  The  author  prefers  a  soft  sponge  eraser  for  this  purpose,  particu- 
larly if  it  was  used  at  the  beginning  instead  of  powder  to  surface  the  cloth 
(page  56  :  2).  Care  should  be  taken  to  rub  between  the  lines  as  far  as 
possible,  rather  than  across  them ;  rubbing  the  lighter  lines  tends  to  make 
them  too  dim  to  print  well  especially  if  the  cloth  has  been  surfaced  with 
.powder.  The  pencil  lines  may  also  be  removed  by  rubbing  the  surface 


of  the  drawing  with  a  cloth  dampened  with  benzine;  the  benzine  does  not 
affect  the  waterproof  ink.  Care  should  be  taken  to  use  only  clean  cloths, 
lest  the  whole  drawing  be  made  dingy.  Many  draftsmen  prefer  the  use 
of  benzine  on  account  of  its  simplicity,  but  for  various  reasons  many 
companies  do  not  furnish  it.  The  author  feels  that  benzine  renders  the 
cloth  more  liable  to  crack  in  handling  and  thus  the  usefulness  of  a  draw- 
ing is  somewhat  impaired. 


CHAPTER  XII 
DRAWING   DIRECTLY  IN  INK  ON  TRACING   CLOTH 

SYNOPSIS:    The  advantages  of  this  method  over  the  method  of  drawing  on  paper 
and  then  tracing  are  shown;  suggestions  are  given  regarding  the  use  of  this  method. 


1.  Method  Recommended.  —  Drawings  may  be  made  on  paper  and 
then  inked  or  traced,  or  they  may  be  made  directly  on  tracing  cloth. 
Some  companies  adopt  one  system,  some  another,  while  still  other 
companies  allow  each  draftsman  to  choose  for  himself.     The  majority 
of  structural  drawings  are  so  similar  to  drawings  already  made  that  it 
is  possible  to  draw  many  lines  in  ink  without  drawing  them  in  pencil 
first.     For  this  reason  the  method  of  making  drawings  directly  on  trac- 
ing cloth  is  recommended  whenever  practicable. 

2.  Some  of  the  companies  that  adopt  the  system  of  penciled  drawings 
employ  tracers,  who  simply  trace  the  drawings  made  by  other  men. 
The  tracers  are  apprentices,  recent  college  graduates,  or  others  of  limited 
experience  who  are  thus  enabled  to  learn  the  points  peculiar  to  the 
structural  company  for  which  they  work  as  well  as  the  usual  conven- 
tions of  the  drafting  room.     Soon  after  a  tracer  becomes  proficient  he 
is  usually  allowed  to  make  drawings  himself,  and  his  place  is  taken  by  a 
new  tracer.     By  this  process  it  is  difficult  to  keep  the  tracing  up  to  the 
proper  standard  and  the  tracings  may  be  issued  in  very  poor  form;  the 
detailer  may  have  to  spend  considerable  time  in  preparing  the  tracings 
for  the  checker,  or  the  checker  may  have  so  many  errors  to  indicate  that 
he  cannot  work  efficiently.     It  is  poor  economy  to  allow  good  men  to 
spend  valuable  time  on  drawings,  only  to  have  much  of  the  meaning  and 
good  appearance  lost  through  careless  tracing;   hence  it  is  often  better 
for  draftsmen  to  make  their  own  tracings.     If  the  draftsman  were  to 
trace  his  own  pencil  drawing  he  would  not  need  to  make  it  quite  so 
complete  as  if  another  person  were  to  trace  it;   but  even  less  penciling 


65 


would  be  required  were  he  to  make  his  drawing  directly  on  the  cloth 
instead  of  on  paper.  In  this  way  he  might  ink  many  lines  and  figures 
without  first  making  them  in  pencil. 

3.  Arguments.  —  Although  it  is  more  serious  to  make  false  lines  in 
ink  than  in  pencil,  this  should  not  prevent  any  careful  draftsman  from 
adopting  this  method  of  inking  much  of  the  drawing  without  previously 
penciling  it.  He  should  cultivate  accuracy  by  strict  attention  to  his 
work,  and  he  should  check  his  work  repeatedly  to  avoid  carrying  a  mis- 
take so  far  that  it  will  entail  extensive  alteration.  When  first  attempting 
this  method,  the  draftsman  should  ink  only  the  lines  and  the  figures 
which  he  is  sure  are  right;  on  subsequent  drawings  he  will  find  that  a 
larger  number  may  be  inked,  and  it  is  believed  he  will  gradually  become 
an  enthusiastic  advocate  of  this  method.  Most  men  who  are  opposed 
to  the  method  have  not  given  it  a  fair  trial;  or  they  have  attempted  to 
ink  too  much,  and  naturally  no  time  has  been  saved.  The  men  who 
still  persist  in  making  complete  pencil  drawings  after  years  of  experience 
are  being  outranked,  for  the  most  part,  by  men  of  equal  ability  who 
work  more  efficiently  by  drawing  directly  in  ink  on  the  cloth.  Even  if 
an  occasional  drawing  has  to  be  retraced  on  account  of  mistakes  made 
in  inking  directly  on  cloth,  this  fact  should  not  be  given  too  much  weight, 
for  the  chances  are  that  the  same  mistakes  would  have  been  made  in 
pencil.  If  that  part  of  the  pencil  drawing  which  is  correct  can  be  pre- 
served and  traced,  so  also  can  the  same  part  of  the  inked  drawing  be  re- 
traced just  as  quickly.  Doubtless  a  little  more  time  is  taken  in  making 
the  original  drawing  in  ink  than  would  be  taken  to  make  it  in  pencil,  but 


PART  II  —  STRUCTURAL   DRAFTING 


since  comparatively  few  drawings  need  be  retraced,  this  loss  is  more  than 
balanced  by  the  time  saved  in  making  other  drawings  directly  in  ink  on 
the  cloth;  this  gain  is  approximately  the  difference  between  the  time 
required  for  drawing  once  in  pencil  and  then  tracing,  and  the  time 
required  for  simply  drawing  in  ink  once. 

1.  Not  all  drawings  are  well  adapted  to  this  method  of  drawing 
directly  in  ink.     If  a  large  number  of  pencil  lines  must  be  drawn,  many 
of  which  may  have  to  be  erased,  better  results  would  probably  be  ob- 
tained by  making  a  pencil  drawing  on   paper.     Sometimes  the  two 
methods  may  be  combined  to  advantage.     Thus,  if  a  drawing  is  so 
complicated  that  the  best  positions  for  the  different  views  must  be 
determined  by  trial,  the  preliminary  work  may  be  done  in  pencil  on 
paper;  but  as  soon  as  the  views  are  finally  located  and  all  necessary 
pencil  lines  drawn,  this  much  of  the  drawing  may  be  traced,  and  the 
remainder  completed  on  the  cloth  just  as  if  all  the  lines  were  so  drawn. 

2.  A  drawing  must  be  carefully  planned  in  advance  if  the  whole  or 
any  part  of  it  is  to  be  inked  without  previous  penciling,  in  order  to  in- 
sure a  good  arrangement  and  to  avoid  crowding.    This  is  not  an  argument 
in  favor  of  a  complete  pencil  drawing,  because  such  preliminary  plan- 
ning should  be  done  also  before  a  pencil  drawing  is  started,  so  as  to 
avoid  the  necessity  of  shifting  the  cloth  while  tracing  to  effect  a  change 
in  the  arrangement.     The  number  of  views  and  the  number  of  dimen- 
sion lines  should  be  determined,  and  also  the  extreme  dimensions  of 
each  view,  including  the  main  member  and  all  projecting  parts.     If  any 
sectional  views  are  to  be  placed  in  breaks  in  other  views  their  positions 
should  be  anticipated  to  avoid  erasing  spaces  for  them  later. 

3.  A  sheet  of  clean  paper  should  be  placed  underneath  the  tracing 
cloth  before  a  drawing  is  started  on  the  cloth;  the  paper  makes  the 
lines  more  distinctly  visible  and  also  covers  the  thumbtack  and  other 
holes  in  the  board  so  that  there  is  less  danger  of  holes  being  punched  in 
the  cloth  by  the  pencil. 

4.  Illustration.  —  As  soon  as  the  number  of  views  and   dimension 
lines  and  the  main  dimensions  of  a  member  are  determined,  points  may 
be  plotted  to  indicate  the  position  of  each  line  that  extends  practically 
the  full  length  or  depth  of  the  member  in  each  view;  pencil  lines  may  be 
drawn  if  necessary  to  show  where  these  long  lines  stop.     Then  these  full 


length  lines,  both  dimension  lines  and  lines  of  the  main  drawing,  may  be 
drawn  in  ink  without  being  drawn  first  in  pencil,  with  a  corresponding 
saving  of  time.  In  case  some  of  the  lines  represent  parts  which  are  to 
be  behind  details  to  be  added  later,  these  lines  may  be  drawn  in  pencil 
or  omitted  altogether  until  the  details  have  been  located ;  then  the  lines 
may  be  inked,  with  dashes  to  represent  the  invisible  portions.  For 
example,  let  us  consider  the  drawing  of  a  plate  girder  with  cover  plates 
(Fig.  102).  Suppose  that  front,  top,  bottom,  and  end  views  are  required 
and  that  the  girder  is  symmetrical  about  the  center  line.  From  a  pre- 
liminary sketch  we  find  how  many  dimension  lines  are  needed.  Points 
may  now  be  plotted  with  due  regard  to  margins  and  spaces  between 
views  to  insure  a  good  arrangement.  Vertically,  these  points  will  show 
the  position  of  (1)  all  full  length  dimension  lines;  (2)  the  three  lines  of 
each  flange  angle  in  the  web  view,  with  the  corresponding  rivet  lines 
(usually  at  the  standard  gage);  (3)  the  eight  lines  in  the  top  view  foi 
the  cover  plate  and  flange  angles,  with  the  corresponding  rivet  lines 
(usually  two  in  number) ;  (4)  same  as  (3)  for  the  bottom  sectional  view. 
Horizontally,  these  points  will  show  the  position  of  (5)  the  left  end  and 
the  center  line  of  the  girder;  (6)  the  cover  plate  and  flange  angle  lines  o) 
the  end  view  which  are  the  same  as  those  in  the  top  view,  and  in  addition 
the  lines  of  the  stiffening  angles  and  their  rivet  lines;  (7)  the  full  depth 
dimension  lines.  Now  the  pen  may  be  filled  and  set  for  fine  lines,  and 
lines  may  be  drawn  in  the  following  order:  (1)  a  continuous  vertical 
line  at  the  end  of  the  girder  drawn  from  the  bottom  view  to  the  top 
view;  (2)  a  dot  and  dashed  line  at  the  center  drawn  from  the  bottorr 
view  to  the  top  view;  (3)  all  horizontal  dimension  lines  and  rivet  lines 
including  Jines  from  the  end  view  to  the  front  view  to  indicate  the  depth 
from  back  to  back  of  flange  angles;  the  rivet  lines  should  extend  beyonc 
the  end  of  the  girder  to  the  proper  dimension  lines;  (4)  the  rivet  line; 
in  the  end  view  and  the  vertical  dimension  lines.  Now  the  pen  may  b( 
set  for  wider  lines,  and  the  following  lines  may  be  drawn :  (5)  the  covei 
plate  lines  of  the  top  view,  provided  the  plate  extends  full  length;  (6' 
the  lines  which  show  the  outstanding  legs  of  the  flange  angles  in  th< 
web  view;  (7)  the  heavy  web  line  and  the  other  lines  of  the  botton 
view,  except  the  cover  plate  lines  which  cannot  be  drawn  until  the  length; 
are  determined ;  (8)  the  vertical  lines  of  the  end  view  (except  the  dashec 


CHAPTER  XII 


DRAWING  DIRECTLY  IN   INK  ON  TRACING  CLOTH 


67 


lines)  and  the  end  line  of  each  of  the  other  three  views;  (9)  the  hori- 
zontal lines  of  the  end  view.  The  pen  may  now  be  set  for  slightly  nar- 
rower lines  (page  37  : 1)  and  the  dashed  lines  may  be  drawn  (10)  for  the 
flange  angles  in  the  top  view,  and  (11)  in  the  end  view.  The  main 
dimensions  may  now  be  recorded  in  ink.  Thus  the  drawing  is  well 
advanced  without  the  use  of  a  single  pencil  line.  As  soon  as  the  stiffening 
angles  are  located,  points  may  be  plotted  to  show  the  three  lines  of  each 
angle  and  the  corresponding  rivet  lines.  The  rivet  lines  may  be  inked, 
then  the  stiffening  angles  in  all  three  views,  and  the  remaining  lines  of 


the  flange  angles  in  the  web  view  which  must  be  dashed  behind  the 
stiffening  angles  now  located.  As  soon  as  the  spacing  of  the  rivets  in  the 
web  view  is  determined  and  the  totals  checked  in  each  panel  as  well  as 
in  the  full  half-length,  the  necessary  rivets  may  be  plotted  and  the  cor- 
responding lines  and  dimensions  inked.  Similarly  the  other  views  can 
be  completed,  and  when  the  cover  plate  lengths  are  definitely  determined 
they  may  be  shown  in  the  top,  front,  and  bottom  views.  The  rivets 
and  holes  may  be  shown,  the  material  may  be  billed  and  the  notes  and 
title  may  be  made  directly  in  ink  without  being  penciled. 


CHAPTER  XIII 
RIVET  SPACING 

SYNOPSIS:  Rivets  must  be  spaced  to  conform  to  general  rules  and  specifications 
which  are  in  common  use;  such  rules  are  given  in  this  chapter.  The  spacing  is  also 
dependent  upon  the  number  of  rivets  required  under  different  conditions,  as  explained 
in  the  chapters  of  Part  III. 


1.  "  Rivet  spacing,"   as  a  general   term,    refers  to   the  dimensions 
which  locate  either  shop  or  field  rivets.     These  dimensions  extend  in- 
variably to  the  centers  of  the  rivets.     "  Rivet  pitch  "  is  a  more  specific 
term  usually  limited  to  the  spacing  which  locates  the  rivets  that  con- 
nect the  component  parts  of  a  built  member  in  the  direction  parallel  to 
the  longitudinal  axis.     This  term  is  most  frequently  applied   to  the 
flange  rivets  of  plate  girders,  in  which  the  pitch  at  different  points  must 
be  determined  from  the  given  loads,  as  explained  in  Chapter  XXXVII, 
page  241. 

2.  General  rules  for  the  spacing  of  rivets  are  given  in  this  chapter 
to  conform  to  those  in  common  use.     The  spacing  is  also  necessarily 
dependent  upon  the  number  of  rivets  required  to  satisfy  the  conditions 
of  loading  and  other  considerations  which  are  discussed  in  different 
chapters  of  Part  III. 

3.  Each  structural  company  adopts  a  set  of  standards  for  the  guid- 
ance of  its  draftsman  in  order  to  make  the  drawings  more  uniform. 
Each  draftsman  should  follow,  whenever  it  is  feasible,  the  standards  of 
the  company  for  which  he  works. 

4.  The  specifications  which  accompany  each  contract  should  be  care- 
fully read,  and  the  rivet  spacing  should  never  violate  any  clause  therein. 
For  the  most  part  the  different  sets  of  specifications  are  quite  similar; 
the  rules  of  this  chapter  conform  to  the  majority  of  them. 

5.  Standard  Gages.  —  The  flanges  of  I-beams  and   channels  are  so 
narrow  that  the  usual  rules  for  clearance  and  edge  distance  cannot  be 


applied  transversely.  Standard  gages  which  will  best  meet  all  require- 
ments are  therefore  adopted.  The  gages  given  in  the  tables  on  pages 
298  to  302  inclusive  are  in  common  use,  although  the  standards  of  some 
companies  differ  slightly.  Standard  gages  for  angles  are  also  adopted 
as  shown  on  page  303.  These  standard  gages  should  be  used  in  all 
places  unless  there  is  good  cause  for  deviation.  However,  it  is  usually 
better  to  change  the  gage  slightly  on  one  drawing  than  it  is  to  make 
the  distance  between  rivets  on  two  or  more  drawings  result  in  sixteenths 
or  eighths,  as  in  connection  angles  for  beams  and  girders  (pages  83  :  6  and 
106:3),  or  in  the  flanges  of  girders  and  columns  (pages  106:3  and  136: 1). 
The  rivets  in  diagonal  bracing  are  often  placed  in  the  centers  of  the 
angles  instead  of  at  standard  gages  (page  139 : 3) .  The  two  rows  of  rivets 
in  a  6-inch  angle  are  often  separated  more  than  usual  to  accommodate 
the  spacing  on  the  members  to  which  they  connect,  as  in  the  base  angles 
of  columns  (Fig.  133)  or  in  struts  (Fig.  147). 

6.  The  minimum  spacing  of  rivets  should  be  such  that  the  strength 
of  the  metal  between  rivets  fully  develops  the  strength  of  one  rivet 
The  minimum  pitches  for  the  rivets  in  the  flanges  of  plate  girders  should 
be  determined  from  the  table  on  page  306  in  accordance  with  the  condi- 
tions of  each  problem,  as  explained  on  page  255: 2.  In  most  other  cases 
it  is  more  convenient  and  sufficiently  accurate  to  use  a  certain  minimun 
space  for  each  different  diameter  of  rivet  regardless  of  other  conditions 
The  values  most  commonly  specified  for  absolute  minimums  are  eithei 
"  three  diameters,"  i.e.,  three  times  the  diameter  of  the  rivets,  or  elsi 


CHAPTER  XIII 


RIVET  SPACING 


69 


the  "  usual  minimum  "  tabulated  on  page  305;  these  specifications  differ 
only  for  the  smaller  rivets.  A  preferred  minimum  is  also  shown  to  be 
used  in  work  of  the  better  class.  These  values  are  based  upon  average 
conditions.  (Compare  with  the  values  for  rivets  in  a  single  line  given 
on  page  306.)  No  two  rivets  should  be  placed  closer  together  in  any 
direction  than  the  proper  minimum  space.  The  minimum  spacing  for 
staggered  rivets  in  tension  members  should  be  taken  from  the  diagram 
on  page  305,  as  explained  on  page  209  : 1. 

1.  The  maximum  spacing  of  rivets  differs  not  only  with  their  diameter, 
but  with  the  type  of  member  and  the  position  of  the  rivets  in  the  mem- 
ber. When  rivets  are  staggered  on  two  lines,  as  in  the  flange  angles  of 
girders  or  columns,  the  maximum  pitches  given  below  refer  to  the  dis- 
tance from  a  rivet  on  one  line  to  the  next  rivet  on  the  other  line  measured 
parallel  to  the  rivet  line  as  if  the  rivets  were  on  a  single  line.  (Compare 
the  next  to  the  last  sentence  of  the  preceding  paragraph),  (a)  In  gen- 
eral, the  maximum  pitch  of  rivets  measured  parallel  to  the  principal 
axis  of  a  member  is  6"  for  1",  |"  or  \"  rivets,  4£"  for  f "  rivets,  and 
4"  for  \"  rivets.  Many  specifications  limit  the  pitch  of  J"  rivets  to  5". 
(b)  The  pitch  should  not  exceed  16  times  the  thickness  of  the  thinnest 
exposed  plate  or  other  shape,  (c)  For  girders,  which  support  moving 
loads  applied  to  the  flanges,  as  crane  girders,  or  stringers  of  bridges  and 
viaducts,  a  maximum  pitch  of  4  or  4|  inches  is  usually  specified  for  the 
flange  rivets,  (d)  The  pitch. of  the  rivets  which  fasten  the  component 
parts  of  a  compression  member  together  should  not  be  more  than  four 
diameters  at  the  ends  of  the  members  and  opposite  the  connections  of 
heavy  loads.  This  close  spacing  should  extend  the  full  depth  of  such 
connections,  and  at  the  ends  for  a  distance  which  is  variously  specified 
as  equal  to  one;  one  and  a  half,  or  two  times  the  width  of  the  member; 
the  mean  value  of  one  and  a  half  may  be  used  unless  otherwise  specified. 
(e)  Rivets  in  tanks  should  not  exceed  about  four  diameters  to  make  the 
joints  watertight.*  (/)  Rivets  which  do  not  transmit  much  axial  stress 
may  be  spaced  farther  apart  than  the  values  given  above;  thus  the 
rivets  which  fasten  skew-back  angles  for  floor  supports  to  the  webs  of 
beams  and  girders  may  be  I'-O"  apart,  rivets  which  connect  stiffening 

*  See  table  of  spacing  for  watertight  joints  in  Ketchum's  "Structural  Engineers' 
Handbook,"  McGraw-Hill  Book  Co.,  Inc.,  New  York. 


angles  to  channel  struts  or  stiffening  channels  to  crane  beams  l'-6", 
countersunk  rivets  in  column  bases  from  9"  to  I'-O",  and  stitch  rivets 
as  indicated  on  page  69  : 4. 

2.  Wide  Cover  Plates.  —  The  rivets  in  the  flange  plates  of  a  compres- 
sion member  are  usually  placed  in  two  rows  unless  the  distance  between 
the  rivet  lines,  measured  at  right  angles  to  the  principal  axis,  exceeds 
forty  times  the  thickness  of  the  outside  plate;    in  this  case  four  rows 
would  be  used.     If  two  or  more  plates  project  3"  or  more  beyond  the 
edges  of  the  angles,  an  extra  row  of  rivets  must  be  used  to  fasten  them 
together,  the  pitch  being  twice  that  of  the  rivets  which  connect  the 
plates  to  the  angles. 

3.  "  Edge  distance  "  is  a  term  applied  to  the  perpendicular  distance 
measured  from  the  center  of  a  rivet  or  hole  to  the  edge  of  any  structural 
shape.     WThen  possible  the  edge  distance  should  be  at  least  one  and  a 
half  diameters,  and  preferably  two  diameters,  as  tabulated  on  page  305. 
This  is  especially  important  in  the  direction  of  the  line  of  stress.     Smaller 
edge  distances  are  unavoidable  in  the  flanges  of  the  smaller  beams 
(page  68  : 5),  and  it  may  seem  best  to  use  them  in  comparatively  light 
work  in  places  where  the  available  space  is  limited,  but  it  is  usually  best 
for  the  novice  not  to  make  such  exceptions  without  due  counsel.     The 
edge  distance  should  not  be  more  than  5"  nor  more  than  eight  times  the 

.  thickness  of  the  thinnest  exposed  plate  or  other  shape. 

4.  Stitch  Rivets.  —  A  member  composed  of  two  angles  should  have 
them  riveted  together  at  frequent  intervals  in  order  that  the  stress  may 
be  distributed  equally  between  the  two  angles.     If  the  angles  are  sep- 
arated on  account  of  connections  to  gusset  plates,  a  washer  is  placed 
between  them  at  each  rivet  in  order  to  maintain  a  uniform  distance 
between  the  angles.     These  equalizing  rivets  with  or  without  washers  are 
called  "  stitch  rivets."     They  need  not  be  dimensioned,  but  the  proper 
number  should  be  shown  or  else  the  approximate  spacing  should  be  noted. 
The  distance  between  the  last  rivet  of  one  connection  and  the  first  rivet 
of  the  next  connection  should  be  divided  approximately  equally.     Stitch 
rivets  are  spaced  from  2'-6"  to  3'-0"  apart  in  tension  members,  but  from 
l'-6"  to   2'-0"  apart  in   compression   members  on  account  of  the  tend- 
ency of  the  latter   to   buckle.     The   specifications   for  railway  bridges 
sometimes  limit  the  spacing  of  stitch  rivets  in  tension  members  to  I'-O". 


70 


PART   II  —  STRUCTURAL  DRAFTING 


1.  Lattice  bars  are  used  in  light  compression  members  or  diagonals 
instead  of  web  plates  or  cover  plates,  and  on  the  under  side  of  chord 
members  where  it  would   be   impractical   to    use    cover  plates.     Tie 
plates  should  be  used  at  the  ends  of  each  group  of  bars.     For  the  sizes 
of  tie  plates  and  lattice  bars,  see  page  216  : 2-3.     For  the  method  of 
billing  and  the  method  of  manufacturing  lattice  bars  see  page  45  :  2. 
For  the  method  of  representing  and  dimensioning  lattice  bars  see  pages 
40:3  and  50:6.      Either    "single   latticing"    or    "double   latticing" 
may  be  used  as  shown  on  page  315,  double  latticing  being  used  when 
the  distance  between  rivet  lines  is  more  than  l'-3".     A  rivet  is  placed  at 
each  intersection  of  double  lattice  bars.     The  inclination  of  double  lattice 
bars  with  the  longitudinal  axis  of  a  member  should  not  be  less  than  45°, 
i.e.,  the  distance  from  center  to  center  of  rivets  in  any  bar,  measured 
parallel  to  this  axis,  should  not  exceed  the  corresponding  distance  meas- 
ured at  right  angles  to  the  axis.     The  inclination  of  single  lattice  bars 
with  the  longitudinal  axis  varies  from  60°  in  important  members  to  45° 
in  comparatively  light  and  unimportant  ones;    for  most  work  an  in- 
clination of  from  50°  to  55°  proves  satisfactory.     When  single  lattice 
bars  are  used  on  opposite  sides  of  the  same  member  the  bars  should 
alternate,  as  shown  in  Fig.  129.     The  clearance  between  the  end  bar 
and  the  tie  plate  should  preferably  be  from  j"  to  1J",  or  else  the  bar 
should  overlap  the  plate  with  a  common  rivet.     The  spacing  for  different 
groups  of  lattice  bars  on  the  same  or  similar  members  should  be  made 
so  that  the  bars  are  interchangeable  as  far  as  possible. 

2.  Practical  Points.  —  (a)  Every  separate  piece  should  contain  at  least 
two  rivets  even  if  one  rivet  is  strong  enough,  because  a  single  rivet  is 
not  sufficient  to  hold  the  piece  in  position  properly.     (6)  Rivets  should 
be  spaced  with  due  regard  to  the  appearance  of  the  finished  member; 
for  example,  a  single  small  pitch  between  two  large  pitches  in  a  girder 
flange  is  conspicuous  (page  70  :  4).     (c)  When  multiple  punches  are  to 
be  used,  the  rivet  spacing  should  be  given  so  that  the  punches  can  be 
used  to  the  best  advantage.     In  multiple  beam  punches  the  spacing  is 
usually  fixed.     In  multiple  plate  punches  the  spacing  may  be  made  to 
correspond  to  the  drawing,  but  the  work  may  be  facilitated  if  the  holes 
for  intermediate  connections  are  made  to  line  up  with  the  other  holes. 
(d)  Templets  are  often  made  to  serve  for  several  different  members; 


this  fact  should  be  borne  in  mind  when  the  rivets  are  spaced.  Long 
lines  of  rivet  spacing  on  similar  members  should  be  kept  alike  as  far  as 
possible,  the  different  spaces  being  kept  near  together,  preferably  at  the 
ends  so  that  different  short  templets  may  be  used  in  conjunction  with 
one  long  one.  The  differences  may  often  be  made  in  the  same  templet 
by  boring  different  sets  of  holes;  the  centers  of  these  holes  should  not 
fall  less  than  \"  apart  or  they  will  interfere  with  each  other. ' 

3.  Usual  Spaces. — The  rivets  which  connect  the  main  component 
parts  of  a  member  are  spaced  as  far  apart  as  is  compatible  with  the  con- 
ditions outlined  in  the  preceding  paragraphs,  in  order  to  minimize  the 
number  of  rivets  to  be  driven.     But  the  rivets  which  connect  one  mem- 
ber to  another,  or  part  of  one  member  to  another  part,  are  placed  at  the 
usual  minimum  or  the  preferred  minimum  distances  as  far  as  possible 
in  order  to  reduce  the  size  of  the  connecting  material. 

4.  Continuous  Rivet  Spacing.  —  The  following  suggestions  may  aid  the 
beginner  in  spacing  long  lines  of  rivets  which  extend  virtually  the  whole 
length  or  depth  of  a  member:  —  (a)  First  locate  all  rivets  which  an 
determined  by  given  conditions,  such  as  those  in  connections  to  othei 
members,  those  near  the  ends  of  compression  members,  or  those  whicl: 
must  line  up  with  other  rivets  on  account  of  fixed  gages  or  working 
lines;   then  complete  the  spacing  of  the  intermediate  rivets  as  follows 
(6)  If  the  number  of  intermediate  rivets  is  determined  by  the  stress 
the  rivets  are  spaced  approximately  equidistantly.     The  available  dis 
tance  is  divided  into  the  proper  number  of  spaces  (one  more  than  th< 
number  of  intermediate  rivets) ;  unless  the  result  is  a  multiple  of  j",  thi 
nearest  \  is  usually  chosen  for  part  of  the  spaces,  another  value  beinj 
used  for  the  one  or  more  remaining  spaces.     Usually  one  odd  space  wil 
serve  to  balance  the  line  satisfactorily  unless  the  spacing  should  b< 
kept  symmetrical  as  in  the  stiffening  angles  of  a  plate  girder  when  tw< 
should  be  used,     (c)  If  the  intermediate  rivets  are  spaced  at  a  fixec 
pitch  (usually  the  maximum  allowed)  as  in  columns  or  chord  members 
the  number  of  such  spaces  is  determined  and  any  remainder  is  noted 
This  remainder  may  be  inserted  as  a  special  space  provided  it  is  large 
than  the  adjacent  space;  otherwise  it  is  better  to  add  it  to  one  or  mor 
of  the  maximum  spaces  and  subdivide  the  sum;   this  should  preferably 
be  arranged  so  that  not  more  than  one  space  results  in  sixteenths,  am 


CHAPTER  XIII 


RIVET  SPACING 


71 


so  that  all  of  the  spaces  are  smaller  than  the  fixed  pitch  but  equal  to  or 
larger  than  the  adjacent  space  for  the  sake  of  appearance.  When  more 
"  balancing  spaces  "  than  one  are  used  they  may  all  be  placed  at  one 
end  of  the  group,  or  part  may  be  placed  at  each  end.  (d)  If  the  rivet 
pitch  changes  at  intervals  as  in  the  flanges  of  plate  girders,  enough  spaces 
of  each  pitch  are  used  to  extend  the  proper  distance  from  the  end  (page 
241  :  5).  Near  the  center,  enough  spaces  of  the  last  pitch  must  be  used  to 
complete  the  total  length;  in  case  a  remainder  is  left,  one  or  more  odd 
spaces  may  be  inserted  at  the  last  change  in  pitch,  but  the  odd  spaces 
should  be  larger  than  one  pitch  and  smaller  than  the  other  for  the  sake 
of  appearance.  The  odd  spaces  should  not  be  placed  at  the  center  of 
the  girder  because  a  few  small  spaces  in  the  middle  of  a  group  of  large 
spaces  would  not  look  well.  The  spacing  should  be  made  symmetrical 
about  the  center  line;  the  center  line  should  therefore  fall  either  at  a 
rivet  or  midway  between  two  rivets,  whichever  gives  the  better  arrange- 


ment of  balancing  spaces.  If  the  girder  is  divided  into  fixed  panels  by 
stiffeners,  care  should  be  taken  that  the  spaces  in  each  panel  total  the 
proper  amount,  and  that  ample  driving  clearance  is  allowed  for  all  rivets 
(page  73  : 5).  (e)  For  the  benefit  of  the  shopmen  sixteenths  and 
eighths  should  be  avoided  whenever  practicable.  For  instance,  rather 
than  make  ten  equal  spaces  in  sixteenths,  eight  or  nine  spaces  can  be 
made  alike  leaving  one  or  two  odd  spaces,  not  more  than  one  of  which 
involves  sixteenths.  (/)  After  a  1  ne  of  rivet  spacing  is  completed  it 
should  always  be  totaled  to  make  sure  that  the  sum  equals  the  proper 
amount;*  similarly  the  sum  of  the  spaces  which  subdivide  any  other 
dimension  should  equal  that  dimension,  (g)  The  multiplication  table 
for  rivet  spacing  on  page  307  may  be  used  to  advantage  in  this  work. 

*  There  is  a  small  adding  machine  (The  Architects'  Calcumeter)  on  the  market, 
which  is  admirably  adapted  to  this  purpose,  but  at  present  its  price  is  beyond  the 
reach  of  the  average  draftsman. 


CHAPTER  XIV 
CLEARANCE,  AND   ERECTION   CONSIDERATIONS 

SYNOPSIS:  There  are  many  points  which  the  draftsman  should  consider  in  order  to 
make  the  erection  of  a  structure  not  only  possible  but  comparatively  easy.  Clearance 
should  be  allowed  so  that  members  or  parts  of  members  may  be  assembled  without 
interference,  and  so  that  rivets  may  be  driven  by  machine. 


1.  Clearance  should  be  provided  wherever  possible  to  facilitate  the 
assembling  of  the  component  parts  of  members  in  the  shop,  and  the 
erection  of  the  whole  members  in  the  field.     Clearance  is  of  greater 
importance  in  field  connections  than  in  shop  work  because  of  the  diffi- 
culty in  handling  the  larger  pieces  which  are  involved  and  which  must 
be  put  into  comparatively  inaccessible  places.     It  is  much  simpler  to 
trim  a  small  piece  in  the  shop  than  it  is  to  cut  a  whole  member  in  the 
field.     The  more  common  places  where  clearance  should  be  provided 
are  (a)  between  the  component  parts  of  a  member,  (b)  between  the  pro- 
jecting parts  of  a  member  and  the  members  to  which  it  is  to  connect, 
(c)  at  the  ends  of  a  member  which  is  to  be  inserted  between  the  faces 
of   the   supporting    members,   and    (d)    between    each    rivet  and    any 
projecting    part  which    might   interfere   with    the    use    of   a    riveting 
machine. 

2.  Provision  for  Overrun.     There  is  often  a  variation  between  the 
actual  size  of  a  structural  shape  and  the  size  indicated  on  the  corre- 
sponding drawing.     This  variation  may  be  the  result  of  the  methods 
of  rolling  the  material  at  the  mills,  especially  angles,  as  explained  on 
page  25  :  1 ;  or  it  may  be  due  to  inaccurate  cutting  either  at  the  mill  or 
at  the  shop.     In  any  event,  due  allowance  should  be  made  so  that  the 
assembling  of  the  different  parts  will  not  be  made  unnecessarily  difficult. 
For  example,  the  rivets  which  connect  the  diagonal  members  of  trusses, 
latticed  girders,  or  bracing  systems  to  the  gusset  plates  should  be  so 
placed  that  these  members  may  be  cut  short  enough  to  avoid  any  inter- 


ference with  the  chords  or  other  members.  This  provides  for  an> 
variation  in  the  lengths  of  the  diagonal  members  or  in  the  depths  or 
widths  of  the  chord  members.  See  pages  76  :  1  and  138  :  5.  Similarly 
I-beams  and  channels  are  ordered  short  enough  to  allow  for  overrur 
as  explained  on  page  88  :  1,  to  avoid  the  necessity  of  recutting  them 
If  the  members  are  assembled  in  the  shop  the  usual  clearance  is  \" 
but  if  assembled  in  the  field  the  clearance  is  increased  to  \" .  Ir 
order  to  eliminate  sixteenths  and  preferably  eighths  from  the  billec 
lengths  of  the  members  the  above  values  may  be  increased  by  -jV"  o 
|",  or  in  some  cases  reduced  by  -fa". 

3.  In  some  places  tight  fits  are  necessary,  but  this  work  involve 
additional  expense  and  should  be  avoided  whenever  possible.     Stiffenm; 
angles  of  plate  girders  are  usually  fitted  so  that  the  outstanding  legs  ar 
in  contact  with  the  flange  angles.     These  angles  must  not  only  be  cu 
carefully  to  length,  but  they  must  be  cut  to  clear  the  curved  fillets  o 
the  flange  angles  (page  26  : 1).     Similarly,  stiffeners  are  used  under  sea 
angles  and  in  similar  places. 

4.  Projecting  parts  should  be  arranged  so  that  they  will  not  interfer 
with   the  erection  of  a  member.     Clearance  should  be  left  betwee 
members  which  connect  independently  to  the  same  member.     One  c 
more  angles  of  a  member  may  have  to  be  cut  shorter  than  the  remainin 
angles,  as  for  example  the  chords  of  LG  2,  Fig.  111.     Similarly  a  men 
ber  may  have  to  be  notched  or  blocked  out  as  in  Figs.  87  and  10 
The  amount  of  clearance  should  be  at  least  \" . 


72 


CHAPTER  XIV 


CLEARANCE,  AND  ERECTION  CONSIDERATIONS 


73 


1.  Erection  Clearance.  —  When  one  member  is  to  frame  at  right  angles 
between  the  faces  of  two  other  members  and  is  to  be  connected  by 
means  of  angles  riveted  to  the  webs,  as  for  example  B  10  (Fig.  87)  and 
S  1  (Fig.  98),  the   extreme  distance  from  back  to  back  of  connection 
angles  should  be  made  less  than  the  clear  distance  between  the  faces  of 
the  supporting  members  in  order  to  allow  "  erection  clearance."     It  is 
not  always  possible  to  allow  sufficient  clearance  to  permit  the  member 
to  be  swung  into  position  without  moving  the  supporting  members; 
for  if  the  ratio  of  the  width  of  a  member  to  its  length  is  large,  the  neces- 
sary clearance  would  be  so  great  that  the  surfaces  could  not  be  drawn 
together  to  make  a  satisfactory  riveted  joint.     But  even  if  the  support- 
ing members  must  be  spread  while  the  other  member  is  being  inserted,  a 
little  clearance  is  desirable  as  a  safeguard  against  an  overrun  which 
would  prevent  restoring  the  supporting  members  to  their  proper  posi- 
tions.    The  amount  allowed  varies  from  -fa"  to  -fg"  at  each  end;   some 
companies  contend  that  -fa"  is  practically  negligible  on  account  of  the 
paint,  scale,  and  careless  shopwork  which  may  counterbalance  it;    but 
from  a  larger  clearance  may  result  loose  joints,  or  else  the  columns  and 
girders  which  support  long  lines  of  such  beams  may  be  drawn  out  of 
plumb.     For  most  work  -fa"  or  J?"  at  each   end  should  be  allowed 
for  erection  clearance;    thus:  in  order  to  make  the  length  back  to  back 
of  angles  free  from  sixteenths,  a  total  clearance  of  TV'  should  be  sub- 
tracted  if   the  clear  distance  between  supports  results  in  sixteenths; 
otherwise  \"  should  be  subtracted.     No  erection  clearance  is  required 
when  one  end  »f  the  member  is  wall  bearing  or  otherwise  free  to  move, 
or  when  the  member  frames  diagonally  between  two  other  members. 

2.  Seat  Angles.  —  The  end  of  a  beam  or  a  girder  should  be  supported 
entirely  by  end  connection  angles,  or  else  by  a  seat  angle  or  some  form 
of  bracket,  but  never  by  a  combination  of  the  two  because  of  the  diffi- 
culty in  making  both  act  at  the  same  time.     Erection  seats  should  be 
provided  to  support  girders  with  end  angles  until  the  rivets  are  driven 
(Fl,  Fig.  99);  erection  seats  may  also  be  provided  for  heavy  beams  or 
for  beams  which  are  to  be  connected  to  opposite  sides  of  a  web  plate  by 
the  same  rivets.     Usually  an. erection  seat  is  shown  \"  lower  than  the 
bottom  of  the  girder  so  that  if  inaccurately  set  it  will  not  prevent  the 
placing  of  the  rivets.     When  seat  angles  or  brackets  carry  the  whole 


load,  top  angles  or  side  supports  should  be  provided  to  prevent  the  beams 
or  the  girders  from  overturning.  Top  angles  should  be  shipped  bolted 
so  that  they  may  be  removed  during  erection  if  desired.  A  clearance  of 
i"  should  be  left  between  the  tops  of  the  beams  and  these  angles  to  pro- 
vide for  any  increase  in  the  depth  of  the  beam  on  account  of  the  spreading 
of  the  flanges  or  the  use  of  worn  rolls  during  manufacture;  a  similar 
clearance  of  \"  should  be  left  between  the  angles  and  the  tops  of  girders. 

3.  Holes  for  anchor  bolts  for  columns  and  girders  should  be  made 
TV  or  |"  larger  than  the  bolts.     This  either  simplifies  placing  mem- 
bers on  bolts  which  are  already  set,  or  else  provides  for  drilling  holes  in 
the  masonry  after  the  steel  work  is  in  position.     The  holes  should  be 
located  with  these  points  in  view. 

4.  Other  Connections.*  —  The  extreme  width  or  depth  of  web  mem- 
bers, top  struts  and  laterals,  and  other  members  which  must  be  inserted 
between  two  gusset  plates,  should  be  made  \"  less  than  the  clear  distance 
between  the  plates,  thus  allowing  a  clearance  of  -fa"  on  each  side.     A 
like  amount  should  be  used  if  possible  at  column  splices  (page  276  :  4). 
\Vhen  plates  must  be  inserted  between  angles  it  is  desirable  to  have  the 
space  between  the  angles  \"  more  than  the  plate  thickness;   when  this 
is  not  feasible,  care  should  be  taken  that  no  shop  rivets  are  placed  in 
either  leg  of  the  angles  which  will  prevent  their  being  spread  sufficiently 
to  allow  the  plates  to  enter.     If  such  rivets  are  required  they  should  be 
left  to  be  driven  in  the  field  (Fig.  135).     Often  splice  plates  and  con- 
nection angles  may  be  held  in  position  by  one  or  more  shop  rivets  (Fig. 
133),  but  if  erection  is  thus  made  more  difficult  it  is  better  to  omit  all 
shop  rivets  and  to  ship  the  pieces  bolted  (Fig.  135). 

5.  Driving   Clearance.  —  Both  shop  and   field   rivets  are  preferably 
driven  by  machine  as  explained  on  page  30  :  4,  and  if  possible  rivets 
should  be  so  located  that  the  machines  can  be  used.     A  careless  drafts- 
man sometimes  locates  rivets  which  can  be  driven  only  with  the  greatest 
difficulty,  if  at  all. 

A  common  mistake  among  novices  is  to  space  the  rivets  in  the  cover  plates  of  columns 
or  girders  independently  of  the  stiffening  angles  on  the  web;  as  a  result  the  outstanding 
legs  of  the  stiffeners  often  interfere  with  the  driving  of  the  rivets  in  the  cover  plates. 

*  See  also  Ketchum's  "Structural  Engineers'  Handbook,"  McGraw-Hill  Book  Co., 
Inc.,  New  York. 


74 


PART   II  —  STRUCTURAL  DRAFTING 


In  order  that  machines  may  be  moved  into  the  proper  position  for  driv- 
ing rivets,  sufficient  driving  clearance  must  be  provided  between  the 
rivet  heads  and  any  projecting  parts  to  allow  for  the  dies  which  form 
the  heads.  The  amount  of  driving  clearance  required  under  different 
conditions  is  given  in  the  tables  at  the  bottom  of  page  304. 

1.  Other  Erection  Considerations.  —  (a)  Too  much  care  cannot  be 
taken  to  insure  the  proper  erection  of  each  member  at  the  site.  Not 
only  should  the  holes  of  one  member  match  exactly  the  holes  of  a  con- 
necting member,  but  the  erectors  should  be  able  to  put  every  member 
into  position  without  interference  and  without  undue  labor.  The  diffi- 
culty of  attaining  this  end  increases  in  proportion  to  the  size  of  a  con- 
tract and  to  the  number  of  detailers  and  checkers  who  work  upon  it 
simultaneously.  (6)  Field  rivets  should  be  so  located  that  they  can  be 
driven  when  the  members  are  in  position;  bent  plates  and  projecting 
parts  of  other  members  are  liable  to  interfere,  (c)  Any  mistake  which 
leads  to  cutting  or  drilling  in  the  field  is  very  expensive,  partly  because 
of  the  lack  of  facilities  but  more  especially  because  of  the  number  of 
skilled  workmen  who  are  delayed  during  the  investigation  which  neces- 
sarily precedes  any  alteration.  If  a  member  must  be  returned  to  the 
shop  for  changes,  or  if  a  new  piece  must  be  made  to  replace  a  member, 
the  delay  in  erection  is  often  very  costly. 

An  actual  blunder  may  be  cited  to  show  the  importance  of  studying  the  structure  as 
a  whole.  Two  girders  at  right  angles  to  each  other  were  to  be  connected  to  the  same 
column,  one  to  the  web  and  the  other  to  the  flange.  Each  connection  would  be  correct 
if  used  independently  or  if  one  of  the  girders  extended  in  the  opposite  direction,  but  the 
detailer  and  the  checker  both  overlooked  the  fact  that  the  two  girders  would  intersect 
and  hence  could  not  be  in  position  at  the  same  time.  It  was  necessary  to  cut  one 
girder  short  and  make  it  frame  into  the  other;  also  to  strengthen  the  other  column  con- 
nection to  support  the  combined  load. 

(d)  Details  should  be  arranged  to  facilitate  erection  whenever  possible, 
but  this  is  especially  important  in  replacements,  such  as  office  and  loft 
buildings,  and  railway  bridges,  so  that  the  old  structures  may  be  left 
intact  until  the  last  possible  moment.  Special  types  of  connections  are 
often  used  for  this  class  of  work  in  order  to  reduce  the  number  of  field 
rivets  (page  89  :2).  (e)  The  draftsman  should  be  familiar  with  common 


methods  of  erection  *  in  order  to  anticipate  special  requirements  for  which 
provision  should  be  made  on  the  drawings.  Rivet  heads  which  pro- 
trude far  enough  to  prevent  swinging  a  member  into  position  should  be 
flattened  or  countersunk  (page  40  :  6),  or  else  left  to  be  driven  in  the  field. 
"  Hand  holes  "  may  have  to  be  bored  through  solid  web  plates  to  give 
access  to  the  inside  of  box  sections  for  driving  rivets.  Similarly,  shop 
rivets  may  be  omitted  from  lattice  bars  or  tie  plates  so  that  they  may 
be  removed  temporarily  (Fig.  129).  Single  field  rivets  at  the  intersec- 
tions of  the  diagonals  of  vertical  bents  may  require  special  stagings  for 
the  riveters.  Such  rivets  are  very  expensive  and  they  should  only  be 
used  when  unavoidable.  (/)  When  the  position  in  which  a  member  is 
to  be  erected  cannot  be  readily  determined  from  the  member  or  from 
the  erection  diagrams,  one  end  of  the  member  should  be  marked  N.,  S.,  E., 
or  W.,  or  otherwise,  to  show  the  proper  position.  Shopmen  should  always 
place  a  member  right  side  up,  before  painting  the  shipping  mark  on  the 
side.  This  system  will  prevent  the  erection  of  a  member  upside  down. 
In  some  cases  it  may  seem  desirable  to  make  the  spacing  of  one  or  twc 
rivets  different  at  the  two  ends  to  prevent  interchange.  Similar  pre- 
cautions should  be  taken  to  avoid  mistakes  in  assembling  connection 
angles  or  other  parts  of  members  which  may  cause  trouble  in  erection. 
(g)  When  two  or  more  members  are  to  be  supported  by  the  same  field 
rivets,  they  must  all  be  erected  before  the  rivets  are  driven.  Such 
conditions  are  usually  apparent  from  the  erection  diagrams,  but  the 
draftsman  should  make  sure  that  any  unusual  connections  are  noted  01 
indicated  on  the  diagram  in  such  a  manner  that  the  erector  will  nol 
drive  any  rivets  prematurely,  (h)  Bridge  details  should  in  general  b( 
arranged  so  that  the  trusses  or  girders  may  be  completely  erected  before 
the  floor  system  is  inserted  or,  conversely,  so  that  the  floor  system  car 
be  completely  erected  before  the  trusses  are  put  in  position,  (i)  Note.1 
should  appear  on  the  erection  diagram  drawing  attention  to  all  drilling 
and  cutting  which  must  be  done  in  the  field,  such  as  holes  in  existing 
structures  for  the  connection  of  new  members.  This  shows  the  erector 
that  such  work  is  expected  of  them  so  that  no  claim  for  extra  remunera 

tion  can  be  made. 

*  See  footnote,  page  20. 


CHAPTER  XV 
LAYOUTS 

SYNOPSIS:  There  are  three  common  types  of  layouts  in  which  the  graphic  method  of 
determining  certain  dimensions  may  be  used  to  better  advantage  than  numerical 
computation. 


LA"  layout "  is  a  preliminary  drawing  made  for  the  purpose  of 
scaling  distances  which  cannot  be  obtained  so  easily  in  any  other  way. 
Layouts  are  used  chiefly  for  determining  the  best  shape  and  size  of 
connection  plates  for  members  which  meet  at  oblique  angles,  with  due 
regard  to  rivet  spacing,  edge  distance,  and  clearance.  A  layout  is  usu- 
ally made  on  a  separate  sheet,  and  having  served  its  purpose  it  is  gen- 
erally discarded  just  as  a  calculation  would  be;  such  a  drawing  need  not 
be  made  so  complete  as  a  working  drawing,  but  it  should  be  drawn  much 
more  carefully  to  scale.  In  order  that  distances  may  be  scaled  with 
accuracy  a  layout  should  be  drawn  to  a  comparatively  large  scale;  for 
most  work  a  scale  of  \\"  —  V  is  satisfactory,  but  3"  =  1'  or  1"  =  1' 
are  often  used.  A  separate  layout  is  usually  made  for  each  gusset 
plate  or  bent  plate  connection,  although  similar  layouts  may  often  be 
combined.  The  term  "  layout "  is  also  applied  to  a  preliminary  drawing 
which  may  afterward  be  completed  for  use  as  a  working  drawing.  Thus, 
the  drawing  of  a  truss,  for  example,  may  be  carried  far  enough  for  the 
draftsman  to  scale  the  lengths  of  all  members  with  sufficient  accuracy 
to  enable  him  to  order  the  material,  and  later  this  layout  may  be 
completed  to  serve  as  a  working  drawing. 

2.  When  Used.  —  A  layout  is  necessary  only  when  the  axes  of  the 
members  intersect  at  angles  other  than  90°,  for  if  members  meet  at  right 
angles  all  dimensions  may  be  determined  easily  by  addition  and  sub- 
traction. Layouts  are  commonly  used  for  practically  all  skew  connec- 
tions, and  for  the  gusset  plates  of  trusses  and  various  forms  of  bracing. 
When  working  drawings  are  made  to  a  scale  of  1"  =  1'  separate  layouts 


are  not  usually  required  because  the  sizes  of  the  gusset  plates  may  be 
determined  with  sufficient  accuracy  from  the  drawings. 

3.  A  simple  layout,  composed  of  a  few  limiting  lines- such  as  edges  and 
ends  of  members,  often  suffices  to  give  the  experienced  draftsman  the 
desired  information,  but  a  novice  can  often  save  time  by  putting  in 
extra  lines  to  show  the  conditions  more  clearly.     A  draftsman  should 
make  a  layout  more  complete  if  it  is  to  be  used  also  by  someone  else. 
If  an  elaborate  layout  is  made  for  use  in  ordering  material,  particularly 
when  conditions  are  rather  unusual,  this  layout  should  be  preserved  for 
the  use  of  the  detailer  and  the  checker.     It  need  be  carried  only  far  enough 
at  first  to  serve  the  purpose  of  the  man  who  orders  the  material,  when 
it  may  be  handed  to  the  detailer  to  be  completed  for  his  use.     Most 
checkers  prefer  to  make  new  layouts  in  order  to  obtain  more  positive 
checks,  particularly  if  inaccuracies  in  plotting  will  seriously  affect  the 
results. 

4.  There  are  three  common  types  of  layout  which  will  serve  for 
illustration,  viz.:    gusset  plates,  lateral  plates,  and  bent  plates.     The 
first  two  terms  are  often  used  interchangeably,  but  for  convenience  they 
will  be  treated  as  separate  types  with  this  distinction:   gusset  plates  are 
used  to  connect  main  members  of  trusses  or  other  members  carrying 
considerable  stress  when  it  is  important  that  their  lines  of  action  meet 
in  a  common  point;   lateral  plates  are  used  to  connect  the  members  of 
bracing  systems  or  light  latticed  girders  in  which  a  single  intersection 
is  less  important  so  that  auxiliary  working  points  may  be  used  for  con- 
venience. 


75 


76 


PART  II  —  STRUCTURAL   DRAFTING 


1.  As  an  example  of  the  first  type  there  will  be  given  the  general 
method  of  procedure  for  making  the  layout  of  a  gusset  plate  which  con- 
nects two  web  members  of  a  roof  truss  to  the  bottom  chord,  each  mem- 
ber being  composed  of  two  angles.  See  Fig.  76.  I.  Determine  the 
slopes  of  the  diagonal  members  as  explained  in  the  next  paragraph  (see 
also  page  115:2).  II.  Lay  down  the  working  lines  (usually  the  rivet 
Hues,  see  page  115  :  2),  of  all  the  intersecting  members  to  the  proper  slopes, 
using  a  scale  of  lj"  =  1'  or  3"  =  1'.  III.  Plot  the  limiting  lines  (out- 
side edges)  of  the  angles,  using  the  proper  gages  (page  68  : 5),  and  showing 
the  backs  of  the  angles  on  the  proper  sides.  IV.  Draw  lines  to  show 
the  desired  clearance  c  (page  72  :  2).  V.  Cut  each  diagonal  angle  normal 

to  its  axis  so  that  the  nearest  corner  will 
fall  in  the  clearance  line  just  plotted. 
Make  sure  that  ample  clearance  is  left 
between  the  diagonals.  VI.  Place  a  rivet 
at  the  desired  edge  distance  e  (page  69  :  3) 
from  the  end  of  each  diagonal  angle;  since 
the  distances  from  these  rivets  to  the  work- 
ing point  are  to  be  dimensioned  on  the 
working  drawing,  it  is  usually  preferable  to 
express  them  to  the  nearest  \" ,  either  the 
amount  of  clearance  or  the  edge  distance 

being  changed,  if  necessary,  to  accomplish  this  result.  VII.  Lay  off 
the  proper  number  of  rivets  (page  231  :  1)  in  each  diagonal  member 
at  the  desired  distance  r  apart;  this  distance  is  generally  made  equal 
to  the  usual  or  the  preferred  minimum  spacing  given  in  the  table  on 
page  305,  so  that  the  resulting  plate  is  not  made  unnecessarily  large. 
VIII.  Space  the  proper  number  of  rivets  in  the  chord  member;  if 
the  chord  is  continuous,  rivets  need  be  provided  only  for  the  difference 
in  the  stress  on  opposite  sides  of  the  plate  (see  page  233  : 2) .  These 
rivets  can  often  be  spread  more  than  those  in  the  diagonals  without 
increasing  the  size  of  the  plate;  the  outer  rivets  should  preferably  be 
placed  at  the  distance  e  from  the  edges  of  the  plate;  this  means  that 
they  can  often  be  projected  down  from  the  last  rivets  in  the  diagonals, 
although  in  that  case  the  shape  of  the  plate  must  be  anticipated  and  per- 
haps the  size  must  be  determined  (see  IX  below)  before  the  rivets  can 


Fig.  76. 


be  located.  If  feasible  one  rivet  should  be  placed  at  the  working  point 
where  it  is  most  effective,  but  care  should  be  taken  that  no  space  exceeds 
the  maximum  allowed  (page  69  : 1).  IX.  Draw  in  the  edges  of  the 
gusset  plate  with  due  regard  to  the  following  points:  (1)  allow  ample 
edge  distance  e  from  each  rivet  to  the  nearest  edge  of  the  plate;  (2) 
leave  no  corners  of  the  plate  projecting  beyond  the  angles,  i.e.,  each 
vertex  should  be  hidden  by  the  angles;  a  corner  which  falls  behind  a 
single  angle  should  preferably  be  made  to  come  on  one  edge  of  the  angle 
for  the  sake  of  appearance,  but  if  between  two  angles  this  does  not 
matter;  (3)  reduce  the  number  of  cuts  to  a  minimum,  for  each  cut 
increases  the  cost  of  the  plate;  (4)  avoid  cuts  with  reentrant  angles, 
for  they  cannot  be  sheared;  they  must  be  cut  by  punching  a  series  of 
connected  holes  and  then  chipping  off  the  remaining  projections  between 
holes  with  a  pneumatic  chisel  (page  14) ;  this  operation  is  reserved  for 
very  exceptional  use  (see  SP1,  Fig.  128);  (5)  make  two  edges  of  the 
plate  parallel  and  a  whole  number  of  inches  apart  if  possible,  so  that 
the  plate  may  be  cut  from  one  of  standard  width  (page  43  :  3) ;  (6)  cut 
across  the  full  width  of  the  plate  if  possible,  so  that  a  number  of  similar 
plates  may  be  cut  without  waste  from  a  long  plate,  by  alternating  the 
cuts  as  shown  in  Fig.  44;  (7)  the  width  of  the  plate  is  usually  the 
shorter  dimension  but  this  may  be  changed  if  desired  on  account  of  (5), 
(6),  or  (8);  (8)  use  as  few  different  widths  of  plates  as  practicable  on 
one  drawing,  and  preferably  on  one  contract;  they  may  then  be  ordered 
or  taken  from  stock  to  better  advantage;  (9)  the  nominal  length  of  the 
plate  as  billed  on  the  drawing  is  the  extreme  dimension  at  right  angles 
to  the  width,  i.e.,  the  dimensions  of  the  including  rectangle  are  given; 
this  length  is  preferably  expressed  to  the  nearest  J"  but  eighths  are 
used;  in  ordering  material  in  multiple  lengths  advantage  should  be 
taken  of  any  gain  which  may  result  from  (6),  for  if  the  extreme  lengths 
were  added  together  more  material  than  is  required  would  be  ordered. 

2.  The  calculation  of  the  slope  or  the  bevel  of  one  line  with  reference 
to  another  line  is  based  upon  similar  right  triangles.  As  explained  on 
page  50  : 7,  the  slope  is  represented  by  the  tangent  of  the  angle  reduced 
to  a  base  of  12",  although  the  actual  value  of  the  angle  is  seldom  used. 
A  system  of  working  lines  is  usually  laid  down  in  such  a  way  that  the 
rectangular  coordinates  of  any  intersection  measured  from  any  other 


CHAPTER  XV 


LAYOUTS 


77 


intersection  may  be  easily  determined.  Often  these  coordinates  are 
dimensioned  on  the  drawing,  or  else  they  may  be  found  from  the  propor- 
tion of  similar  triangles.  These  coordinates  form  the  two  legs  of  a 
right  triangle,  in  which  the  slope  and  often  the  length  of  the  hypotenuse 
are  required.  The  tangent  of  the  smaller  angle  of  the  triangle  is  found 
by  dividing  the  length  of  the  shorter  leg  by  the  length  of  the  longer  leg; 
if  this  division  is  effected  by  means  of  a  table  of  logarithms  arranged  by 
feet,  inches,  and  fractions  of  inches,  the  resulting  tangent  will  be  ex- 
pressed as  desired  in  inches  and  fractions  of  inches  (to  the  nearest  six- 
teenth), corresponding  to  a,  base  of  a  unit  foot  (12  inches).  If  the 
length  of  the  hypotenuse  is  required  also,  it  should  be  calculated  at  the 
same  time  as  the  slope  by  means  of  parallel  tables  of  logarithms  and 
squares  *  as  illustrated  by  the  following  problem.  In  Fig.  148  the  holes 
along  the  diagonal  edges  of  M  1  and  M  2  are  referred  to  the  working 
line  of  the  supporting  angle.  The  given  coordinates  are  3'-7j"  and 
10'-2^".  The  corresponding  slope  and  length  of  the  diagonal  as  shown 
on  the  drawing  are  obtained  as  follows: 


Length 

Logarithm 

Square 

3'-7J" 
10'-2J" 

0.55680 
1.00895 

12.9900 
104.2101 

(difference)    9.54785 
slope  =  4j"  in  12" 

(sum)  117.  2001 
length  =  10'-9H" 

Note  that  the  tables  are  expressed  to  thirty-seconds  to  facilitate  the 
selection  to  the  nearest  sixteenth  of  the  desired  slope  or  length  from 
the  corresponding  logarithm  or  square. 

1.  Lateral  plates  are  commonly  used  for  lateral  bracing  in  bridges, 
diagonal  bracing  in  buildings,  in  place  of  gusset  plates  in  light  latticed 
girders,  or  wherever  the  stresses  are  so  small  that  a  slight  deviation 
from  a  single  point  may  be  made  in  the  intersection  of  the  lines  of  action 
of  the  members.  An  auxiliary  system  of  working  lines  is  drawn  through 
the  end  rivets  of  the  diagonals.  The  two  principal  advantages  of  this 

*  A  copy  of  Smoley's  "Parallel  Tables  of  Logarithms  and  Squares,"  McGraw-Hill 
Book  Co.,  Inc.,  New  York,  should  be  included  in  the  equipment  of  every  structural 
draftsman. 


type  of  plate  connection  are  (1)  that  the  clearance  between  members 
can  be  made  more  nearly  equal  with  a  corresponding  reduction  in  the 
size  of  the  plate,  and  (2)  that  a  comparatively  simple  layout  may  be  made; 
in  fact  the  desired  information  may  often  be  obtained  easily  without  a 
layout.  This  type  of  connection  is  illustrated  by  a  plate  in  a  'atticed 
girder,  as  shown  in  Fig.  77.  I.  The  rectangular  coordinates  which 
locate  the  end  rivets  of  the  diagonals  are  usually  made  the  same  for 
the  upper  and  the  lower  ends  of  the  diagonals  so  that  the  plates  may  be 
made  alike  or  similar.  II.  For  most  systems  of  diagonal  bracing  in 
which  the  leg  of  the  diagonal  is  3"  or  more,  the  rivets  are  placed  on  the 
center  line  of  the  leg  in  order  to  make  all  clearances  nearly  equal;  for 
latticed  girders  and  small  diagonals  the 
standard  gage  is  used,  and  thus  when  pro- 
vision is  made  for  the  proper  clearance  for 
the  corner  at  the  back  of  an  angle,  a  larger 
clearance  will  be  left  on  the  opposite  side, 
since  the  gage  is  larger  than  the  remaining 
distance.  III.  The  slope  of  the  diagonals 
cannot  be  calculated  until  the  end  rivets 
are  located,  and  hence  the  position  of  the 
corners  of  the  angles  relative  to  the  end 
rivets  is  unknown;  it  is  customary  to  allow 

sufficient  space  in  any  direction  for  the  maximum  distance  from  the 
rivet  to  the  farther  corner  of  the  angle.  This  distance  is  the  hypo- 
tenuse of  a  small  right  triangle  one  leg  of  which  is  the  gage  (page  68  : 5), 
and,  the  other  the  edge  distance  e  (page  69  : 3) ;  this  may  be  found 
from  the  diagram  on  page  313,  or  from  &  full-sized  layout.f  IV.  The 
vertical  distance  (usually  to  the  nearest  £")  from  the  end  rivets  in  the 
diagonals  to  the  rivet  line  in  the  chord  may  now  be  found  by  adding 
three  component  parts,  (1)  the  edge  distance  (leg  minus  gage)  of  the 
chord  angle,  (2)  the  desired  clearance  (page  72  : 2),  and  (3)  the 
diagonal  distance  found  in  III.  Similarly  the  horizontal  distance 
between  the  end  rivets  of  the  two  diagonals  is  twice  the  distance  found 
in  III,  plus  the  clearance;  in  latticed  girders  this  distance  may  be 

t  A  convenient  table  for  use  in  spacing  the  end  rivets  in  diagonals  is  given  by 
E.  Feldman  in  The  Engineering  News-Record,  Jan.  16,  1919. 


Fig.  77. 


78 


PART  II  —  STRUCTURAL  DRAFTING 


changed  slightly  as  explained  on  page  109  :  1.  V.  Either  of  two. 
methods  may  be  used  for  the  remainder  of  the  problem;  (1)  a  layout 
may  now  be  made  of  the  working  points  already  established  and 
the  remaining  distances  and  the  size  of  the  plate  may  be  determined 
graphically  as  outlined  for  gusset  plates  in  steps  VII,  VIII,  and  IX, 
page  76  : 1;  or  (2)  the  required  data  may  be  found  without  a  complete 
layout,  as  follows:  VI.  From  the  proper  number  of  spaces  r  in 
each  diagonal  find  the  corresponding  horizontal  and  vertical  coordi- 
nates; these  may  be  found  (1)  from  simple  layouts  drawn  separately; 
(2)  from  the  main  working  drawing  upon  which  the  working  lines  have 
been  plotted  to  scale;  the  diagonal  distances  may  be  scaled  along  the 
proper  working  lines  and  the  corresponding  components  measured  with- 
out drawing  any  extra  lines;  or  (3)  by  placing  a  straight-edge  in  the 
proper  position  on  the  diagram  on  page  313,  and  then  reading  the  desired 
coordinates.  VII.  The  dimensions  of  most  lateral  plates  may  be  found 
arithmetically  by  the  proper  combination  of  the  edge  distances  and  the 
distances  found  in  IV  and  VI;  when  diagonal  cuts  are  used  the  posi- 
tions of  the  corners  of  the  plate  may  be  determined  from  a  few  lightly 
penciled  lines  on  the  main  drawing  (see  VI  (2)  above) . 

1.  In  bent-plate  work,  a  layout  is  often  necessary  in  order  to  deter- 
mine the  shape  and  the  size  of  the  connecting  plate.  Such  a  layout  is 
made  of  the  developed  plate,  i.e.,  the  plate  before  it  is  bent.  The 
bend  line  is  plotted  and  parts  of  the  members  to  be  connected  are  drawn 
in  proper  relation  to  a  definite  point  in  this  bend  line,  not  in  their  actual 
relation  to  each  other.  The  rivets  and  holes  may  be  laid  out  to  the 
best  advantage  in  each  member  and  then  the  plate  may  be  formed 
around  these  rivets  and  holes  according  to  the  suggestions  given  under 
IX,  page  76  : 1.  Such  layouts  are  used  for  special  skew  work  beyond 


Beif$  PI.  8"x  -j-'i  IL2 

iz'isii* 


the  range  of  this  book;  *  they  are  not  required  for  ordinary  bent  plate 
work  in  which  the  holes  and  the  edges  of  the  plate  are  laid  off  either 
parallel  or  perpendicular  to  the  line  of  bend,  and  in  which  the  dimen- 
sions for  the  plate  are  determined  numerically.  See  Figs.  78,  93,  and 
149.  When  bent  plates  connect  to  web  plates,  it  is  usually  better  to 
refer  dimensions  to  the  center  lines  of  webs  as  working  lines  instead 
to  the  faces  of  the  bent  plates,  as  shown 
in  the  above  figures.  The  drawing  is 
thus  simplified  although  a  corresponding 
burden  is  imposed  upon  the  templet 
maker;  but  the  method  is  more  direct 
and  there  are  fewer  sources  of  error. 
Dimensions  should  be  so  given  that  they 
truly  represent  the  desired  measurements ; 
only  distances  which  are  parallel  to  the 
line  of  bend  can  be  dimensioned  in  an 
oblique  view  of  a  plate,  i.e.,  in  the  por- 
tion of  a  plate  which  is  not  parallel  to 
the  plane  of  the  drawing.  See  page  141 :  4. 

Care  should  be  taken  to  place  rivets  far  enough  from  the  line  of  benC 
so  that  they  can  be  driven  after  the  plate  is  bent.  If  only  one  bent 
plate  is  used  it  is  better  to  place  it  on  the  obtuse-angle  side  rather 
than  on  the  acute-angle  side.  Bent  angles  may  sometimes  be  used 
instead  of  plates  if  they  are  not  bent  more  than  about  3"  in  12";  the 
line  of  bend  is  likely  to  be  at  the  edge  of  the  fillet  instead  of  at  the 
vertex,  so  that  larger  bends  are  unsatisfactory. 

*  For  illustrations  see  the  author's    "Hip  and  Valley  Rafters,"  John  Wiley 
Sons,  Inc.,  New  York. 


Fig.  78. 


CHAPTER  XVI 
MARKING   SYSTEMS 

SYNOPSIS:  An  identification  mark  is  assigned  to  each  member,  and  this  mark  is 
used  on  the  drawing,  on  different  lists  and  diagrams,  on  the  templets,  and  on  the  steel. 
Similar  marks  may  be  used  on  the  component  parts  of  a  member  for  use  in  the  shop. 


1.  There  are  two  kinds  of  marks  in  common  use  in  structural  work, 
the  one  "Assembling  Marks  "  or  "Piece  Marks,"  and  the  other  "Ship- 
ping Marks"  or  "Erection  Marks."     Assembling  Marks  are  used  on  the 
small  component  parts  of  a  member  to  facilitate  their  fabrication  in  the 
shop.     Shipping  Marks  are  used  on  the  completed  members  such  as 
beams,  girders,  or  sections  of  trusses,  as  they  are  shipped  from  the  shop 
to  the  site,  to  serve  for  identification  in  the  drafting  room,  in  the  order 
office,,  in  the  shop,  in  shipment,  and  in  erection. 

ASSEMBLING   MARKS 

2.  The  assembling  marks  usually  originate  in  the  drafting  room, 
where  they  are  put  on  the  drawings;   in  some  companies  they  originate 
in  the  templet  shop,  where  they  are  indicated  on  the  blueprints  with 
colored  pencil,  and  then  the  prints  are  passed  on  to  the  structural  shop. 
In  either  case,  the  marks  are  painted  on  the  templets,  and  also,  after 
the  holes  have  been  laid  out  from  the  templets,  the  marks  are  painted 
on  the  steel  to  aid  the  fitters  in  assembling  the  parts.     The  use  of 
assembling  marks  enables  the  templet  maker  to  make  a  single  templet 
for  a  detail  which  occurs  on  many  different  sheets,  although  this  may 
be  done  to  a  lesser  degree  when  assembling  marks  are  not  used.     No 
further  mention  will  be  made  of  any  system  of  assembling  marks  which 
may  be  arranged  between  the  templet  makers  and  the  fitters,  for  it  has 
no  bearing  upon  the  drafting  room. 

3.  When  Used.  —  The  draftsman  should  ordinarily  avoid  the  use  of 
assembling  marks  unless  some  apparent  benefit  will  be  derived.     The 


79 


benefit  to  the  draftsman  will  depend  largely  upon  the  system  used,  but 
the  benefit  to  the  shop  will  be  in  proportion  to  the  number  of  times 
the  same  detail  is  repeated,  especially  if  on  different  sheets.  In  some 
instances,  the  use  of  assembling  marks  may  increase  the  cost  of  the 
drawings,  but  this  may  be  offset  by  the  reduced  cost  of  the  shop  work, 
particularly  in  large  contracts.  Assembling  marks  are  not  given  to 
the  main  component  parts  of  a  member,  but  only  to  those  details  which 
occur  more  than  once  on  the  same  or  different  sheets.  When  there  are 
only  a  few  details  of  the  same  nature  on  a  sheet,  there  is  less  need  of 
assembling  marks  than  when  many  similar  pieces  occur  on  the  same 
member  to  confuse  the  fitters.  Moreover,  the  sheet  number  and  the 
shipping  mark  (page  80  :  6)  are  painted  on  each  piece,  and  frequently 
the  assembling  marks  are  superfluous.  Only  large  contracts  with  many 
details  require  the  use  of  assembling  marks.  Occasionally,  as  in  plate 
girder  work,  for  example,  it  is  convenient  for  the  draftsman  to  use 
assembling  marks  on  some  parts,  as  the  st'ffeners  or  fillers,  in  order  to 
save  repeating  the  dimensions  and  sizes,  even  though  marks  are  not 
used  on  the  remainder  of  the  contract  (see  Fig.  102  or  103). 

4.  Many  structural  companies  use  systems  of  assembling  marks  which 
differ  from  each  other  in  minor  details,  but  the  principles  underlying 
most  of  them  are  essentially  the  same.  The  assembling  mark  immedi- 
ately follows  the  billed  size  of  the  piece,  and  consists  of  three  parts,  viz: 
(1)  a  characteristic  letter  which  indicates  the  nature  of  the  piece,  (2)  a 
specific  letter  (or  number)  which  distinguishes  the  piece  from  others  of 
the  same  nature,  and  (3)  the  number  of  the  sheet  where  the  detail  is 


80 


PART  II  — STRUCTURAL   DRAFTING 


first  shown.  The  letters  should  be  lower  case  to  distinguish  the  assem- 
bling marks  from  the  shipping  marks.  The  use  of  assembling  marks  is 
illustrated  by  many  of  the  drawings  of  this  book,  as  for  example  Figs. 
102  and  116. 

1.  The  first  letter  indicates  the  style  of  the  detail  and  should  prefer- 
ably be  suggestive,  as  for  example:  —  6  =  bottom  seat  angles  for  beam 
connections,  /  =  fillers,    m  =  miscellaneous   angles,   p  =  miscellaneous 
plates,  s  =  stiffening  angles,  t .—  top  angles  for  beam  connections,  and 
w  =  light  web  members.     Other  letters  are  used  for  various  pieces,  as 
a  =  base  or  cap  angles  of  columns,  c  =  cap  plates,  base  plates  or  splice 
plates,  h  =  bent  plates  or  angles,  y  =  lattice  bars,  etc.;    these  are  not 
so  significant  as  the  first  group,  and  accordingly  are  not  so  generally 
used  since  each  company  adopts  its  own  code.     Some  companies  even 
differentiate  between  stiffeners  which  are  fitted  at  both  ends  and  those 
which  are  fitted  at  one  end  only,  or  between  fillers  with  two  rows  of 
holes  and  those  with  only  one. 

2.  The  second  letter  (or  number  in  some  systems),  is  used  to  show 
the  difference  between  similar  details  on  a  sheet.     For  instance,  the  end 
stiffeners  of  a  plate  girder  might  be  marked  sa,  the  next  pair  sb,  and 
other  different  ones  sc,  etc.,  double  letters  being  used  when  the  alphabet 
is  exhausted,  as  saa,  sa6,  sac,  etc.     The  letters  i,  1,  o,  q,  and  u  are  usually 
omitted  because  they  are  not  readily  distinguishable. 

3.  The  sheet  number  refers  to  the  sheet  where  the  piece  is  first  de- 
tailed.    On  this  sheet  the  number  after  the  letters  of  the  mark  is  often 
omitted;  it  may  be  understood  that  the  men  in  the  shop  are  to  consider 
the  number  in  the  corner  of  the  sheet  to  be  a  part  of  each  mark,  unless 
another  number  is  given,  and  much  time  may  thus  be  saved.     For  illustra- 
tion, if  a  filler  was  first  detailed  on  sheet  6,  where  it  might  be  marked 
simply  fd,  the  shopmen  would  mark  the  templet  and  the  steel  -fd  6;  if  a 
filler  exactly  like  it  occurred  on  sheet  8,  it  would  be  marked  on  the 
drawing  fd  6  instead  of  fd,  to  show  that  it  was  detailed  on  sheet  6  and  to 
prevent  the  shopmen  from  marking  it  fd  8,  as  they  would  if  the  sheet 
number  were  omitted.     For  the  convenience  of  all  concerned,  the  piece 
should  be  completely  dimensioned  and  billed  once  on  each  sheet,  but  in 
all  other  positions  on  a  sheet  the  dimensions  and  the  billing  may  be 
omitted.     The  assembling  mark  is  placed  near  the  detail  in  each  posi- 


tion.    The  dimensions  for  all  field  rivets  are  sometimes  repeated  to 
simplify  comparison  with  those  of  connecting  pieces. 

4.  All  pieces  which  are  identical  should  be  given  the  same  mark,  and, 
conversely,  pieces  should  have  different  marks  if  they  are  not  inter- 
changeable.    Not  all  companies  indicate  rights  and  lefts  (page  81  :  2), 
in  assembling  marks,  but  expect  the  templet  maker  to  distinguish  them 
by  means  of  the  drawing.     It  seems  preferable,  however,  for  the  drafts- 
man to  complete  the  system  if  it  is  to  be  used  at  all,  and  to  indicate 
rights  and  lefts  on  the  drawing  (see  Fig.  104). 

5.  Sometimes  a  summary  of  assembling  marks  is  placed  in  the  corner 
of  each  sheet  giving  the  number  of  pieces  of  each  mark  required  for 
the  members  to  be  made  from  that  sheet.     A  number  is  added  to  the 
sheet  where  each  piece  is  first  detailed,  to  show  the  total  number  re- 
quired for  the  entire  contract.     While  this  method  is  of  convenience  to 
the  templet  maker,  it  is  not  to  be  recommended  unless  it  is  possible  to 
complete  all  drawings  of  similar  members  before  any  are  sent  to  the 
shop.     Otherwise,  later  drawings  will  refer  to  sheets  already  in   the 
shop  with  a  corresponding  change  in  the  totals;    revised  prints  must 
then  be  issued  —  a  practice  which  should  be  reserved  for  unforeseen 
corrections  or  alterations. 

SHIPPING  MARKS 

6.  The  shipping  marks  should  be  clearly  shown  on  the  detailed  draw- 
ings.    From  the  time  the  draftsman  determines  the  shipping  mark  of  a 
member,  until  the  member  is  in  its  final  position  in  the  structure,  it  is 
known  by  this  mark.     The  mark  appears  on  the  drawing,  on  the  order 
bills,  the  shop  bills,  the  shipping  bills,  and  the  rivet  lists,  and  it  is  painted 
on  the  templets  and  on  the  individual  pieces  of  steel  of  which  the  mem- 
ber is  composed.     The  mark  is  preserved  when  the  completed  member 
is  painted  before  shipment,  and  it  serves  an  important  function  during 
erection  in  enabling  the  erector  to  place  the  member  in  the  proper  posi- 
tion, as  indicated  by  a  similar  mark  placed  on  the  erection  diagrams 
which  are  prepared  by  the  draftsman. 

7.  In  general  a  shipping  mark  is  composed  of  two  parts,  viz:   a  char- 
acteristic letter  or  letters  and  a  specific  number,  as  S  14,  or  LG  2.     Capi- 
tal letters  are  used  to  distinguish  clearly  shipping  marks  from  assem- 


em- 


CHAPTER  XVI 


MARKING   SYSTEMS 


81 


bling  marks  (page  79  :  4).  As  far  as  possible  the  letters  should  be 
suggestive  of  the  type  of  member,  as  for  example,  C  =  columns,  G  = 
girders,  EP  =  end  post,  etc.  For  a  list  of  letters  commonly  used  for 
different  members,  see  page  324.  A  special  system  of  marks  is  used 
for  office-building  construction  in  order  to  indicate  the  floor  numbers,  as 
explained  on  page  81  :  5.  Truss  members  are  usually  marked  accord- 
ing to  a  system  of  panel  point  letters,  as  explained  on  page  82  :  1. 

1.  Shipping  marks  should  be  marked  conspicuously  on  the  drawing 
either  just  below  the  drawing  (Fig.  87)  or  at  the  right  of  the  sheet 
above  the  title  (Fig. 100).     When  several  different  members  are  shown 
on  the  same  sheet  the  marks  may  be  tabulated  in  a  "Required  List  " 
above  the  title  (Fig.  135) ;  when  these  members  are  represented  by  differ- 
ent drawings  on  the  sheet,  each  drawing  should  bear  the  corresponding 
shipping  marks,  as  shown  in  Fig.  140. 

2.  Rights  and  Lefts.  —  All  members  which  are  identical  should  bear 
the  same  shipping  mark  (except  in  office  buildings,  page  81  :  5),  and 

conversely  no  two  members  should 
be  marked  the  same  unless  they 
are  interchangeable.  When  pieces 
are  exactly  opposite  they  may  be 
marked  "Right"  and  "Left,"  one 
drawing  serving  for  both.  The 
drawing  should  be  made  for  the 
e  member  marked  "Right";  the 

[=^======  ^       "Left"  member  is  then  made  as 

'Reversed  about  BB 
*  '       if  the  drawing  were  reversed;    the 

marks  should  be  placed  on  the 
erection  diagram  accordingly.  No 
indication  of  rights  and  lefts  need 
be  made  on  the  main  part  of  the 
drawing,  the  only  difference  being 
made  in  the  list  of  members  re- 
quired, where  the  rights  and  lefts  are  distinguished  by  adding  the 
capital  letters  R  or  L  to  the  shipping  mark,  as  in  B  4,  Fig.  85,  and  C  5, 
Fig.  137.  Before  marking  pieces  right  and  left,  the  draftsman  should 
satisfy  himself  that  the  pieces  are  really  opposite,  and  that  there  are  no 


Right 


C 


Reversed  about  A  A 


Left 
Reversed  aOout  CC 


Fig.  81.   Rights  and  Lefts. 


other  differences.  The  novice  frequently  imagines  that  two  members 
are  opposite  when  in  reality  they  are  interchangeable  if  inverted  or 
turned  end  for  end.  A  conception  of  rights  and  lefts  may  be  gained 
from  Fig.  81.  If  all  the  details  are  reversed  about  any  one  of  the  three 
axes  of  symmetry  a  left  is  obtained,  but  if  they  are  reversed  about  any 
two  axes,  one  reversion  counteracts  the  other  and  the  piece  remains  un- 
changed. If  a  member  were  placed  in  front  of  a  mirror  the  right  would 
be  represented  by  the  real  member  and  the  left  by  the  reflected  image. 

3.  Members  Combined.  —  One  drawing  may  be  made  to  serve  for 
several  different  members  if  the  differences  are  properly  indicated  or 
noted,   as    explained    on    page   53  : 4.     Members  which   are   marked 
rights  and  lefts  may  be  combined  with  other  members  on  a  drawing, 
but  the  details  should  be  shown  just  as  if  only  the  rights  were  combined. 
It  is  unnecessary  to  indicate  "R  "  or  "L  "  in  the  various  notes  on  the 
drawing,  but  simply  the  remainder  of  the  mark,  since  all  notes  must 
necessarily  apply  to  both  the  "R  "  and  the  "L."     For  example,  in  Fig. 
135,  the  required  list  calls  for  columns  C  1R  and  C  1L,  but  each  individual 
note  on  the  drawing  refers  to  C  1  only,  with  the  understanding  that  it 
applies  to  both,  and  that  C  1R  is  made  like  the  drawing,  and  C  1L  is  made 
opposite.     No  member  should  be  marked   "Left"   unless  there  is  a 
corresponding  "Right."     (See  next  paragraph.) 

4.  Opposites.  — •  Two  members  which  cannot  be  marked  R  and  L 
because  they  are  not  exactly  opposite  may  be  so  nearly  opposite  that 
they  can  be  combined  on  the  same  drawing  to  advantage.     They  must 
be  given  different  marks  and  in  the  required  list  the  mark  of  one  must 
be  followed  by  the  word  "Opposite,'1  as  in  R  22,  Fig.  93.     Such  a  mem- 
ber would  be  made  as  if  the  drawing  were  reversed,  in  much  the  same 
manner  as  a  "left  "  is  made,  but  in  accordance  with  special  notes  or 
dimensions.     All    details   which    apply   only   to    the   member   marked 
"Opposite  "  should  be  drawn  in  the  proper  relation  to  all  other  parts, 
subject  to  reversion  with  the  rest  when  the  member  is  made. 

5.  A  special  system  of  marks  is  usually  adopted  in   office-building 
construction  in  order  to  distinguish  between  members  which  are  erected 
at  different  stages.      Usually   the   columns  are  erected   in   two-story 
lengths  and  the  two  corresponding  tiers  of  beams  and  girders  are  erected 
at  the  same  time;   all  the  derricks  are  then  raised  two  stories  and  the 


82 


PART   II  —  STRUCTURAL  DRAFTING 


process  is  repeated.  Members  should  be  shipped  approximately  in  the 
order  of  erection;  this  is  usually  necessary  because  of  the  lack  of  storage 
facilities,  and  is  desirable  because  it  simplifies  erection.  All  identical 
beams  and  girders  in  any  one  floor  bear  the  same  mark;  identical  beams 
and  girders  in  different  floors  may  be  combined  on  the  same  sketch  and 
have  the  same  specific  number,  but  they  must  bear  different  floor  marks 
(see  C  17,  D  17,  E  17,  Fig.  92).  Office-building  columns  are  numbered 
consecutively  according  to  some  definite  system  for  convenience  in 
finding  a  particular  number;  thus  no  two  columns  bear  the  same  mark 
even  though  they  may  be  interchangeable.  The  columns  are  num- 
bered the  same  on  all  plans  so  that  each  column  bears  the  same  specific 
number  as  the  column  directly  above  or  below  it  but  the  floor  marks 
are  different.  Two  methods  of  marking  office-building  members  are  in 
common  use.  First  Method.  Each  beam  should  bear  the  character 
"#  "  for  "Number  "  (instead  of  a  letter),  followed  by  a  specific  number 
and  by  the  floor  number,  thus:  #25  —  3rd  FL.,  or  #3  —  ROOF.  Each 
girder  should  bear  the  letter  G  followed  by  a  specific  number  and  by  the 
floor  number,  thus:  G  2  —  BASMT.,  or  G  5  —  4th  FL.  Each  column 
should  bear  the  abbreviation  "COL.,"  and  a  specific  number,  followed 
in  parentheses  by  the  numbers  of  the  floors  between  which  it  extends, 
thus:  COL.  11  (0-2),  or  COL.  19  (10-ROOF).  Second  Method.  A 
capital  letter  is  assigned  to  each  floor  or  tier  of  beams,  as  A  =  basement, 
B  =  first  floor,  C  =  second  floor,  and  so  on  up  to  R  =  roof;  the  letters 
I,  0,  and  Q  are  omitted  to  avoid  confusion  with  similar  letters  or  figures. 
Each  beam  should  bear  a  floor  letter  followed  by  a  specific  number, 
thus:  D  25,  or  R  3  (see  also  Fig.  87).  -Each  girder  should  bear  the  letter 
G  followed  by  a  specific  number  and  by  the  floor  letter  or  number,  thus: 
G  2  —  A-TIER,  or  G  5  —  4th  FL.  Each  column  should  bear  the  let- 
ters of  the  tiers  of  beams  which  it  supports,  followed  by  a  specific  num- 
ber, thus:  AB  11,  or  MR  19  (see  also  Fig.  133).  If  another  story  were 
inserted  between  tiers  M  and  R,  the  top  section  would  become  R  19  or 
preferably  M  NR  19,  depending  upon  the  length. 

1.  Truss  members  are  marked  according  to  the  letters  of  the  panel 
points  or  apices  between  which  they  extend.  In  bridge  trusses  the 
upper  apices  are  marked  U  1,  U  2,  etc.,  and  the  lower  apices  are  marked 
L  0,  LI,  L2,  etc.;  these  marks  are  so  arranged  that  L  1  is  directly 


under  U  1,  etc.,  as  shown  in  the  sketch  on  page  324.  Web  members 
are  marked  with  the  panel  marks  at  their  ends,  thus:  L  2-U  1,  or  L  2-U  2 
(Figs.  126  and  129).  Chord  members  need  not  have  the  letter  L  or  U 
repeated,  thus:  L  2-3,  or  U  1-3  (Figs.  125  and  124).  End  posts  are 
usually  marked  EP  (instead  of  L  0-C7  1),  (Figs.  122  and  127).  For 
the  sake  of  uniformity,  drawings  are  made  for  the  members  in  the  left- 
hand  half  of  the  far  truss  and  the  members  should  be  marked  right  and 
left  accordingly. 

2.  A  roof  truss  is  usually  erected  as  a  whole  in  order  to  save  falsework. 
A  small  truss  may  be  shipped  completely  riveted,  but  a  larger  truss 
must  be  shipped  in  sections;    these  sections  are  assembled  and  riveted 
together  on  the  ground  and  the  entire  truss  is  then  lifted  into  position. 
A  whole  truss  is  marked  on  the  erection  diagrams  with  the  letter  T 
followed  by  a  specific  number,  but  unless  the  truss  is    shipped    com- 
pletely assembled,  each  member  or  truss  section  must  bear  a  separate 
shipping  mark.     An  assembling  diagram  is  shown  on  the  sheet  where 
the  truss  is  detailed  (Fig.  116),  and  sometimes  this  is  duplicated  on  a 
smaller  sheet  more  convenient  for  the  erector.     The  apices  are  lettered 
as  illustrated  in  the  sketch  on  page  324,  the  letters  being  the  same  in 
both  halves  with  the  exception  of  A  and  X.     When  one  half  of  a  truss 
is  shipped  in  one  section  it  is  marked  either  AH  or  XH  followed  by  a 
specific  number,  the  half  trusses  on  one  side  of  the  building  being  marked 
AH  to  differentiate  them  from  those  on  the  other  side  which  are  marked 
XH,  thus:    AH2R  or  XH  3  (Fig.  116).     When   smaller  sections  than 
one-half  of  a  truss  are  shipped  they  are  marked  by  the  three  letters  at  the 
extremities  followed  by  a  specific  number,  thus :  A  CG  3,  or  CEF  2.    When 
single  members  are  shipped  separately  they  are  marked  with  the  letter  at 
their  ends,  followed  by  a  specific  number,  thus:  HH  1  or  FL  2  (Fig.  116). 

3.  Straight  tie  rods  and  sag  rods  may  be  identified  by  their  lengths. 
On  the  drawings  and  erection  diagrams  these  lengths  are  expressed  in 
inches  inscribed  in  a  circle  to  avoid  confusion  with  other  marks.     It  is 
unnecessary  to  paint  the  number  on  each  individual  rod.     Bent  rods, 
and  main  bracing  rods  are  marked  in  the  usual  manner  with  an  X  fol- 
lowed by  a  specific  number. 

4.  Special  direction  marks  may  be  added  to  members  in  order  to 
facilitate  proper  erection,  as  explained  in  (/),  page  74  :  1. 


CHAPTER  XVII        s 
BEAMS 

SYNOPSIS:  In  the  preceding  chapters  are  given  the  more  general  fundamental  prin- 
ciples of  drawing.  These  are  followed  by  chapters  in  which  are  given  more  specific 
information  applicable  to  the  drawing  of  the  more  common  types  of  members.  In 
this  chapter  are  given  the  types  of  connections,  the  methods  of  dimensioning,  and 
other  conventions  and  practical  points  peculiar  to  I-beams  and  channels. 


1.  A  beam  is  a  member  which  resists  flexure  or  cross  bending.     Usually 
it  is  placed  in  a  horizontal  position  and  is  subjected  to  vertical  loads. 
A  simple  beam  rests  upon  two  supports  and  all  its  loads  are  applied 
between  the  supports.     A  cantilever  beam  receives  part  or  all  of  its  loads 
upon  the  portion  of  the  beam  which  extends  beyond  the  supports.     A 
cantilever  beam  may  rest  upon  two  supports  and  extend  beyond  one  or 
both,  or  it  may  be  fixed  at  one  end  by  a  masonry  wall,  or  by  other  means, 
and  be  unsupported  at  the  other  end.     A  continuous  beam  rests  upon 
more  than  two  supports  and  its  use  should  be  avoided  if  practicable.     A 
simple  beam  is  encountered  in  practice  more  frequently  than  any  other 
structural  member. 

2.  Generally  speaking,  a  beam  is  composed  of  a  single  piece,  exclusive  of 
details,  and  is  usually  of  wood,  of  steel,  or  of  concrete.     In  steel  construc- 
tion, a  member  which  is  made  of  more  than  one  main  piece  but  which 
acts  like  a  beam,  is  termed  a  girder,  see  Chapter  XVIII,  page  95. 

3.  The  forms  of  steel  beams  which  are  most  commonly  used  are  the 
I-beam  and  the  channel.     Since  I-beams  are  frequently  called  simply 
"beams,"  care  should  be  taken  to  avoid  ambiguity  between  the  general 
term  which  applies  either  to  I-beams  or  to  channels,  and  the  specific  term 
which  refers  to  I-beams  only.     In  this  book  the  term  "beams  "  includes 
both  I-beams  and  channels. 

4.  In  order  to  reduce  the  cost  of  making  structural  drawings  for 
beam  work,  the  details  of  which  are  usually  similar  and  comparatively 


simple,  most  companies  furnish  printed  forms.*  Upon  these  forms  are 
outlined  I-beams  or  channels,  some  with  the  top  and  bottom  views, 
and  some  without.  A  few  dimension  lines  are  also  printed,  the  others 
being  added  by  the  draftsmen  as  required.  The  use  of  these  forms 
allows  only  one  size  of  sketch  regardless  of  the  actual  dimensions  of  the 
beams  to  be  drawn,  and  consequently  the  drawings  cannot  be  drawn  to 
scale.  It  is  best,  if  practicable,  to  plot  the  detaiZs  according  to  the 
scale  which  most  closely  corresponds  to  the  depth  of  the  beam,  but  to 
estimate  the  distances  between  the  details  so  that  they  are  approxi- 
mately proportional  to  the  total  length.  A  complete  sketch  should  be 
drawn  to  scale  when  the  number  of  details  or  the  complexity  of  special 
connections  warrants  it;  a  blank  sheet  of  the  same  size,  and  with  the 
same  printed  headings  is  provided  for  this  purpose. 

5.  Beams  are  supported  either  by  masonry  walls,  or  else  by  connections 
to  other  beams,  to  girders,  trusses,  columns,  etc.     For  any  given  type  of 
connection  the  details  used  by  the  different  companies  are  quite  similar. 

6.  Standard  Connection  Angles.  —  The  beams  of  mill  buildings  and 
similar  structures  are  connected  to  each  other  so  generally  by  means  of 

*  In  order  to  enable  the  student  to  become  familiar  with  blanks  similar  to  those 
used  in  practice,  the  author  has  prepared  several  forms  suitable  for  use  in  any  uni- 
versity, copies  of  which  may  be  obtained  from  the  publishers,  John  Wiley  and  Sons, 
Inc.,  New  York.  The  drawings  of  this  chapter,  before  one-half  reduction,  were  made 
on  these  forms. 


S3 


84 


PART   II  —  STRUCTURAL   DRAFTING 


angles  riveted  in  the  shop  to  the  ends  of  the  supported  beams  that  most 
companies  have  adopted  standard  connection  angles.  In  1912  the 
American  Bridge  Company  adopted  the  connection  angles  shown  on 
pages  298  and  300.  These  differ  from  the  older  forms  shown  on 
pages  299  and  301  in  the  size  of  the  angles  and  hi  the  number  and 
the  spacing  of  the  rivets,  but  they  were  adopted  only  after  sufficient 
tests  had  been  made  to  justify  their  use.  They  have  since  been  incor- 
porated in  the  handbook  of  the  Carnegie  Steel  Company,  and  are  used 
in  the  drawings  of  this  book.  The  older  forms  are  distinguished  in  the 
tables  as  "Lackawanna  "  angles  although  similar  standards  are  shown 
in  the  handbooks  of  the  Cambria,  Phoenix,  Pennsylvania,  and  Jones  & 
Laughlin  Steel  Companies,  and  others,  and  formerly  were  used  by  the 
American  Bridge  Company.  Connection  angles  for  Bethlehem  beams 
are  shown  on  page  302.  In  the  new  form  mentioned  above  the  vertical 
spacing  is  3"  without  exception,  while  in  the  old  form  both  1\"  and  3" 
are  used.  On  account  of  the  different  web  thicknesses  either  the  gage 
in  the  angles  or  else  the  distance  between  the  holes  must  vary.  In  the 
old  form  a  standard  gage  is  used,  with  a  variable  distance  center  to 
center  of  holes,  while  in  the  new  form  the  "constant  dimension  system  " 
is  employed,  i.e.,  the  distance  between  holes  is  maintained  65"  regard- 
less of  the  resulting  gages.  The  constant  dimension  system  is  some- 
times used  with  the  old  form  angles  as  well,  both  types  being  shown  in 
the  tables  on  pages  299  and  301.  The  constant  dimension  system 
is  recommended,  for  it  simplifies  the  details,  especially  when  beams 
of  different  web  thicknesses  frame  on  opposite  sides  of  a  supporting 
web  with  rivets  in  common.  The  system  is  also  well  adapted  to  inter- 
departmental short-cuts  (see  below),  but  it  involves  a  larger  number  of 
standard  templets.  This  number  is  reduced  in  the  plants  of  some  com- 
panies by  the  use  only  of  the  gages  which  are  multiples  of  eighths. 
Where  the  tables  give  values  for  b  in  sixteenths  these  companies  use  the 
eighth  above  on  one  side  of  the  web,  and  the  eighth  below  on  the  other 
side,  thus  throwing  the  beam  ^"  off  center.  In  the  drawings  of  this 
book  gages  are  used  as  they  appear  in  the  tables. 

1.  Fig.  85  shows  an  I-beam  and  a  channel  detailed  according  to 
three  different  methods.  The  upper  modified  method  is  the  one 
adopted  in  this  book,  the  lower  one  shows  the  old  form  of  connection 


angles,*  while  the  middle  one  shows  the  American  Bridge  Company's 
method  which  is  greatly  simplified  by  means  of  interdepartmental 
understandings,  f  The  students  should  learn  first  the  more  general 
method,  but  later,  as  draftsmen,  they  must  make  their  drawings  con- 
form to  the  standards  of  the  companies  for  which  they  work. 

2.  In  the  modified  method  the  connection  angles  should  be  dimen- 
sioned and  billed  as  shown  in  B  1  and  B  4,  Fig.  85.  The  center  of  each 
connection  should  be  located  from  one  flange  of  the  beam  even  though 
the  angles  are  placed  centrally  on  the  beam  as  is  usually  the  case.  The 
holes  in  the  webs  to  provide  for  the  standard  connection  angles  of  other 
beams  are  dimensioned  in  groups,  and  then  the  centers  of  the  groups  are 
located  vertically  arid  horizontally.  Note  that  the  holes  of  each  group 
are  not  definitely  dimensioned  from  these  centers  but  it  is  assumed  that 
the  holes  are  placed  symmetrically  about  the  center  lines.  This  is  one 
of  a  few  such  assumptions  made  in  structural  drafting,  most  dimensions 

*  The  older  forms  of  connection  angles,  as  shown  on  pages  299  and  301  or  with  slight 
modifications,  are  used  by  many  companies.  The  vertical  spacing  for  all  but  the 
18",  20",  and  24"  I-beams  is  2|".  The  gage  in  the  outstanding  legs  is  constant,  and 
the  distance  between  holes  variable,  as  shown  by  the  values  of  a,  page  299.  Two 
methods  of  dimensioning  the  connections  of  channels  are  used,  the  one  giving  the  total 
distance  center  to  center  of  holes  as  for  I-beams  but  the  other  giving  the  distances 
from  the  holes  to  the  backs  of  the  channel  webs,  as  shown  in  B  G,  Fig.  85.  The  values 
of  h  from  the  back  of  the  web  to  the  holes  in  the  angle  on  the  opposite  face  of  the  web 
are  given  on  page  301.  With  these  exceptions  the  method  of  detailing  is  similar 
to  the  modified  method  outlined  in  this  chapter. 

f  The  principle  differences  between  the  American  Bridge  Company's  method  and 
the  method  outlined  in  this  chapter  may  be  summarized  as  follows:  —  Channels  are 
preferably  drawn  with  the  flanges  on  the  far  side  to  correspond  to  their  position  on  the 
rollers  in  front  of  the  multiple  punch;  the  connection  angles  are  neither  billed  nor 
dimensioned;  the  horizontal  distances  from  center  to  center  of  connections  are  omitted, 
only  the  extension  figures  being  used  except  in  complicated  work;  the  distances  from 
the  flange  to  the  first  holes  of  standard  connections  are  given  instead  of  the  distances 
to  the  centers  of  the  groups,  because  the  holes  are  punched  by  a  multiple  punch  and  no 
templets  are  used;  the  holes  for  tie  rods  and  for  anchors  are  not  dimensioned  the 
former  being  marked  "T"  to  distinguish  them  from  the  beam  connections;  single 
angle  connections  are  marked  "M"  for  distinction;  beams  under  15"  which  are  coped 
to  beams  of  the  same  size  are  shown  coped  but  are  not  noted;  the  overall  dimension, 
the  ordered  length,  the  number,  the  mark,  and  the  size  are  combined  on  one  of  the 
dimension  lines,  as  shown  in  B  2  and  B  5,  Fig.  85. 


CHAPTER  XVII 


BEAMS 


85 


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Fig.  85.   Comparison  of  Different  Methods  of  Detailing  Beams. 


86 


PART 


II  —  STR 


UCTURAL  DRAFTING 


being  made  more  definite  to  permit  of  no  misunderstanding.  Holes  other 
than  those  for  standard  connection  angles  may  be  dimensioned  as  in 
B  12,  Fig.  87,  or  C  17,  Fig.  92.  The  vertical  dimensions  should  be 
referred  to  one  flange  only,  because  the  actual  depth  of  a  beam  does  not 
always  agree  exactly  with  the  nominal  depth,  on  account  of  the  wearing 
of  the  rolls  or  of  the  spreading  of  the  flanges  while  they  are  cooling. 
Usually  they  are  referred  to  the  bottom  flange,  except  when  it  is  desirable 
to  maintain  a  uniform  elevation  of  the  tops  of  the  beams  by  referring  them 
•  to  the  top  flange  instead. 

1.  Where  it  is  impossible  to  use  two  connection  angles  on  account 
of  interference  with  other  connections,  a  single  larger  angle  may  be 
substituted.     For  the  lighter  beams,  single  angles  are  shown  in  the 
tables  on  pages  298  and  300,  but  for  heavier  beams  similar  connections 
should  be  used  only  when  they  are  especially  designed  to  satisfy  the 
given  conditions,  as  discussed  on  page  234 : 2.     When  a  single  angle  is  used 
care  should  be  taken  to  show  by  means  of  full  or  dashed  lines  upon  which 
side  of  the  web  the  angle  is  to  be  placed.    See  B  1,  Fig.  85. 

2.  When  beams  of  different  depths  frame  on  opposite  sides  of  a  web, 
standard  connections  should  be  used  if  possible,  even  though  the  angles 
have  to  be  placed  above  or  below  the  centers  of  the  beams  in  order  to 
accommodate  the  rivets  which  are  in  common.     If  the  beams  are  not  in 
the  same  vertical  plane  but  too  close  to  permit  the  use  of  independent 
standard  connections,  special  connections  must  be  provided;   often  two 
angles  with  special  gages,  or  a  single  angle  connection  mentioned  in  the 
preceding  paragraph,  may  be  used. 

3.  Standard  angles  are  designed  for  usual  conditions,  but  they  should 
not  be  used  for  short  spans  or  for  beams  with  concentrated  loads  near 
the  ends  unless  the  number  of  rivets  is  found  sufficient  according  to  page 
234  : 2.     If  the  number  has  to  be  increased,  care  should  be  taken  that  the 
angles  are  not  made  so  long  that  they  will  interfere  with  the  curved 
fillets  of  the  beams  (page  26  : 1). 

4.  Beams  are  usually  shown  full  length  even  though  they  are  sym- 
metrical about  the  center  lines  (compare  page  34  : 5).     If  the  connection 
angles  are  alike  at  both  ends  of  a  beam,  the  duplication  of  dimensions 
and  also  of  the  end  view  may  be  avoided  by  noting  the  right  end  "Same 
as  other  end,"  as  in  B  10,  Fig.  87.     See  also  page  53  :1.     The  angles 


should  be  shown  in  the  web  view  in  order  that  beams  with  connection 
angles  at  both  ends  may  be  clearly  distinguished  from  beams  with  no 
angles  or  beams  with  angles  at  one  end  only.  The  angles  should  be 
billed  at  each  end  for  the  convenience  of  the  billers. 

5.  The  centers  of  the  groups  of  holes  for  all  intermediate  web  con- 
nections are  located  horizontally  in  two  ways.  For  the  convenience  of 
the  men  in  the  drafting  room  the  dimensions  are  given  from  center  to 
center  of  groups  and  from  the  ends  of  the  beam  to  the  centers  of  the 
end  groups  (see  next  paragraph).  For  the  convenience  of  the  men  in 
the  shop  in  spacing  the  small  templets  on  the  steel  from  one  setting  of 
the  tape,  and  also  for  the  use  of  the  inspector,  "  extension  figures "  are 
given  to  indicate  the  distance  from  the  left  end  of  the  beam  to  the  center 
of  each  group.  All  of  these  extension  figures  may  be  placed  on  a  single 
dimension  line,  provided  single  arrow  heads  are  so  arranged  that  each 
dimension  extends  from  the  nearest  arrow  head  on  the  right  to  the  first 
arrow  head  on  the  left  that  faces  the  opposite  way,  i.e.,  the  one  at  the  left 
end,  see  B  1,  Fig.  85.  It  is  not  necessary  to  repeat  the  dimension  at 
the  left  end;  it  is  usually  given  on  the  line  of  extension  figures.  Simi- 
larly, it  is  unnecessary  to  insert  the  overall  dimension  on  the  line  of 
extension  figures,  provided  it  is  given  elsewhere.  Beams  which  have 
connection  angles  on  one  end  only,  should  be  drawn  with  the  angles  at 
the  left  end  so  that  the  extension  figures  extend  to  .the  more  definite  end 
(compare  page  88: 1).  The  center  of  each  group  of  holes  is  located  on  the 
drawings  even  though  the  connection  is  for  a  channel.  Since  the  spacing 
of  channels  on  the  erection  diagrams  is  given  to  the  backs  of  the  webs  and 
not  to  the  center  lines,  as  for  I-beams,  it  is  important  that  this  difference 
be  taken  into  consideration  when  the  dimensions  which  locate  channel 
connections  are  determined.  When  the  web  thickness  is  given  in  six- 
teenths on  page  300  or  301,  the  proper  value  to  use  for  one-half  the  web 
thickness  may  be  obtained  by  subtracting  TV"  from  the  value  of  c. 

6.  The  length  of  a  beam  with  connection  angles  at  both  ends  is  the 
distance  from  back  to  back  of  angles.  This  is  made  less  than  the  clear 
distance  between  the  surfaces  of  the  supporting  members  in  order  to 
allow  the  proper  erection  clearance,  as  explained  on  page  73  :  1.  In 
determining  this  length  the  draftsman  usually  obtains  the  necessary 
data  from  an  erection  diagram  upon  which  the  dimensions  extend  to  the 


CHAPTER  XVII 


BEAMS 


87 


DRAFTING  FORM  1 


UNIVERSITY   BRIDGE  COMPANY 


B RANCH 

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Fig.  87.    Typical  Beams. 


88 


PART  II  —  STRUCTURAL  DRAFTING 


centers  of  the  webs  of  I-beams,  girders,  and  columns,  but  to  the  backs 
of  the  webs  of  channels.  For  the  convenience  of  the  detailer  and  the 
checker  it  is  we!l  to  record  at  each  end  of  the  overall  dimension  line  the 
distance  from  the  back  of  the  angle  to  the  working  line  of  the  supporting 
member  shown  on  the  diagram;  these  distances  may  then  be  used  in 
determining  the  overall  length  and  also  the  distance  from  each  end  to  the 
first  intermediate  connection  mentioned  in  the  preceding  paragraph.  In 
general,  the  distance  from  the  working  line  to  the  back  of  the  angle  will 
be  the  sum  of  the  erection  clearance,  usually  Ty  (see  below),  and  the 
distance,  if  any,  from  the  working  line  to  the  surface  of  the  supporting 
member  to  which  the  beam  is  to  be  connected.  For  example,  if  a  beam 
connects  to  the  web  of  an  I-beam,  the  distance  from  the  center  of  the  web 
to  the  back  of  th'e  angle  will  equal  one-half  the  web  thickness  +  TV"  =  c, 
values  for  which  are  given  on  pages  298  and  299.  If  a  beam  connects 
to  the  web  of  a  channel,  the  distance  will  either  be  -fa",  or  else  the 
whole  web  thickness  +  tV"  =  c'  depending  upon  whether  the  beam  con- 
nects to  the  outer  face  (back)  or  to  the  inner  face  of  the  channel  web; 
values  for  c' are  given  on  pages  300  and  301.  If  the  main  dimension 
from  back  to  back  of  angles  results  in  sixteenths,  it  is  preferable  to 
decrease  it  to  the  nearest  eighth  (page  34  :  6),  and  to  increase  the 
distance  from  the  working  line  to  the  back  of  the  angles  at  one  end  of  the 
beam  to  correspond.  When  connection  angles  are  used  at  only  one  end 
of  a  beam  no  erection  clearance  is  required,  so  the  distance  from  the  back 
of  the  angles  to  the  working  line  should  be  reduced  accordingly. 

1.  Beams  are  sawed  at  the  rolling  mills  to  the  ordered  lengths  while 
still  hot,  and  each  beam  must  be  cut  into  the  desired  lengths  before  the 
following  one  leaves  the  rolls;  the  lengths  cannot,  therefore,  be  measured 
with  great  precision  and  all  lengths  must  be  accepted  if  within  the  "  mill 
variation  "  of  f "  specified  by  the  steel  companies.  All  beams  should  be 
ordered  in  multiples  of  \"  in  such  lengths  that  they  can  be  used  even 
though  they  overrun  or  underrun  f";  greater  allowance  is  often  made 
to  avoid  recutting  the  beams  in  the  shop  in  case  of  greater  overrun.  The 
material  is  ordered  usually  before  the  detailed  drawings  are  made,  but 
with  due  consideration  of  the  types  of  connections  to  be  used.  The  de- 
tailer must  make  his  drawings  conform  to  the  ordered  lengths  if  possible. 
The  ordered  length  is  given  underneath  the  detail  along  with  the  number 


of  pieces  and  the  size  of  the  beam  is  billed  as  indicated  on  page  44  :  2-3, 
and  as  illustrated  in  the  typical  drawings  of  this  chapter.     When  no  con- 
nection angles  are  used  the  overall  dimension  must  manifestly  equal  the 
ordered  length ;  but  when  connection  angles  are  used  at  one  or  both  ends 
the  overall  dimension  is  assumed  to  extend  to  the  backs  of  the  angles  and 
the  ordered  length  may  differ.     Usually  the  beams  are  ordered  to  the 
nearest  \"  so  that  each  pair  of  angles  will  project  about  \"  beyond  the  end 
of  the  beam;  thus,  the  ordered  length  of  a  beam  with  angles  at  one  end  is 
about  \"  (from  f  to  f)  less  than  the  overall  length,  while  the  ordera 
length  of  a  beam  with  angles  at  both  ends  is  about  1"  (from  f  to  \\)  le& 
than  the  overall  length.     In  order  to  use  printed  forms  to  the  best  ac 
vantage  the  angles  are  shown  on  the  drawing  flush  with  the  ends  of  th 
beams,  as  indeed  they  may  be;  the  only  indication  that  they  are  not  flus 
is  the  discrepancy  between  the  ordered  length  and  the  overall  length 
When  conditions  require  that  the  end  of  the  beam  must  not  extend  withi 
a  certain  distance  of  the  backs  of  the  angles,  the  minimum  "set  back  "  i 
indicated  as  in  H  14,  Fig.  87.     Beams  are  detailed  with  the  understanc 
ing  that  unless  noted  otherwise  an  end  without  connection  angles  i 
allowed  to  vary  \"  from  the  position  indicated  on  the  drawing;   othe 
variations  may  be  noted  at  the  end,  as  for  example  ±f  in  B  4,  Fig.  85,  o 

—  0  in  B  7,  Fig.  87;  if  no  variation  is  allowed  the  end  may  be  marked 
or  else  the  dimension  may  be  marked  "exact."  Wall  bearing  ends  (se 
next  paragraph)  need  not  be  noted  as  a  rule,  for  it  is  evident  that  greate 
variation  than  \"  is  permissible. 

2.  Beams  which  are  supported  by  masonry  walls  must  rest  on  meta 
bearing  plates  in  order  that  the  loads  may  be  distributed  over  th 
proper  area  (page  288  :  2).  The  size  of  the  plate  required  for  eac 
beam  is  given  in  the  tables,  pages  298  to  302,  and  the  width  of  th 
plate  (the  smaller  dimension)  indicates  the  length  of  the  bearing,  i.e. 
the  distance  which  the  beam  must  project  on  the  wall.  The  bearin: 
plates  are  not  attached  to  the  beams,  but  the  latter  are  held  in  place  b; 
some  form  of  anchor  which  is  imbedded  in  the  masonry.  The  ancho 
most  commonly  used  is  the  Government  anchor,  which  is  a  f"  ro 
bent  as  shown  on  page  316.  A  hole  must  be  provided  for  this  in  th 
beam  2"  from  the  end,  placed  centrally  in  the  web  or  else  on  line 


CHAPTER  XVII 


BEAMS 


89 


other  holes  (page  91  :  2).  An  angle  anchor  is  sometimes  used,  as 
shown  on  page  316.  The  bearing  plates  and  anchors  are  shipped 
separately,  and  are  not  shown  on  the  drawing  (see  page  174  :  1).  A 
wall  bearing  is  indicated  conventionally  on  the  drawing  by  lines  which 
represent  masonry,  as  shown  in  B  4,  Fig.  85,  and  M  15,  Fig.  87. 

1.  Coping.  —  When  a  beam  is  to  frame  into  the  web  of  an  I-beam  or 
the  flange  face  of  a  channel  web,  it  may  be  necessary  to  cut  away  part 
of  one  or  both  of  the  flanges  to  prevent  interference  with  the  flange  of 
the  beam  to  which  the  beam  connects;  the  end  of  the  beam  thus  cut  is 
said  to  be  "coped."  A  beam  may  be  coped  by  means  of  standard  dies 
set  in  a  punch,  or  by  means  of  an  oxy-acetylene  flame.  Standard  coping 
is  shown  on  the  drawing  without  dimensions,  but  the  size  of  the  connect- 
ing beam  should  be  noted,  thus:  "Cope  to  18"  I  55#";  the  weights 
of  beams  less  than  15"  deep  may  be  omitted  because  no  difference  is 
made  in  the  amount  of  coping  for  the  different  weights,  thus:  "Cope 
to  12"  L_l ."  When  beams  are  drawn  on  blank  sheets  the  coped  portions 
may  be  omitted,  but  when  printed  forms  are  used  it  is  not  feasible  to 
erase  the  printed  lines  and  so  the  coped  portions  are  blackened  as  in 
B  4,  Fig.  85.  The  blackened  portion  need  not  be  scaled  but  for  the 
'sake  of  appearance  the  distance  from  the  end  of  the  beam  to  the  vertical 
line  drawn  between  the  two  lines  of  the  flange  should  be  estimated  to  be 
about  one-half  the  width  of  the  flange  shown  in  the  end  view;  the  slop- 
ing line  should  be  drawn  parallel  to  the  sloping  line  of  the  end  view; 
i.e.,  to  the  standard  bevel  of  2  in  12,  as  shown  in  B  4,  Fig.  85  and  B  10, 
Fig.  87.  Care  should  be  taken  to  show  the  proper  flange  blackened, 
i.e.,  the  top  flange  when  the  beams  are  flush  top,  the  bottom  when  flush 
bottom,  and  both  when  beams  of  the  same  depth  are  flush  both  top  and 
bottom.  Every  cope  should  be  indicated,  for  a  beam  will  be  coped  only 
where  distinctly  shown;  when  the  connection  angles  at  one  end  are 
referred  to  those  at  the  other  end,  the  note  "Same  as  other  end  "  does 
not  necessarily  apply  to  the  coping,  although  in  case  it  does  not  apply 
it  is  better  to  modify  the  note  to  read  "Connection  angles  same  as  other 
end."  One  note  at  each  end  for  the  size  of  beam  to  which  a  beam  is 
coped  is  sufficient  whether  one  or  two  flanges  are  to  be  cut;  in  case  one 
:>nd  is  noted  "Same  as  other  end  "  the  size  need  not  be' repeated  if  the 
<ame,  but  it,  should  be  given  if  it  is  different  or  if  one  end  is  not  referred 


to  the  other.  In  general,  the  note  "Same  as  other  end  "  should  be  used 
only  to  save  considerable  duplication  (page  86  :  4) ;  it  should  not  be 
used  when  dimensions  or  notes  can  be  repeated  with  no  more  work. 
It  is  sometimes  necessary  to  "block  out  "  the  flange  of  a  beam  according 
to  special  dimensions,  as  shown  in  B  7,  and  H  14,  Fig.  87  or  R  21, 
Fig.  93.  It  is  difficult  to  block  out  one  side  of  the  flange  flush  with 
the  web  because  the  curved  fillet  pushes  the  beam  away  from  the  cutter 
sufficiently  to  leave  a  slight  projection;  the  drawing  should  specify 
whether  or  not  it  is  necessary  to  chip  off  this  projection  as  in  B  12,  Fig. 
87,  or  R  21,  Fig.  93. 

2.  In  office-building  construction  great  stress  is  laid  upon  speed 
during  erection  (see  (d)  page  74  :  1),  and  the  beam  connections  are 
designed  accordingly.  Seat  angles  are  used 
wherever  feasible,  because  the  supporting 
rivets  may  be  driven  in  the  shop,  and  be- 
cause each  beam  may  be  erected  indepen- 
dently of  any  other  beam;  this  is  impossible 
when  two  beams  are  framed  to  the  opposite 
sides  of  a  web  by  means  of  standard  con- 
nection angles  with  field  rivets  in  common. 
The  type  of  connection  shown  in  Fig.  89  (a)  is  used  for  beams  supported 
by  other  beams  or  girders  which  are  deep  enough  to  provide  space  for 
the  seat  angles;  the  whole  loads  are  carried  by  the  seat  angles,  designed 
according  to  page  235  :  1,  and  the  webs  are  bolted  to  the  side  angles 
to  hold  the  beams  in  place;  ordinarily  no  holes 
are  provided  in  the  seat  angles.  Such  connec- 
tions with  and  without  stiffening  angles,  are 
shown  in  Fig.  104,  and  B  12,  Fig.  87,  is  a  typical 
beam  supported  in  this  way.  The  type  of  con- 
nection shown  in  Fig.  89  (b)  is  used  for  beams 
which  connect  to  columns;  the  seat  is  designed  to 
carry  the  whole  load  (page  232  : 2) ,  and  a  top 


Fig.  89  (a). 


Fig.  89(6). 


angle  is  used  simply  to  hold  the  beam  in  position  and  to  stiffen  the  con- 
nection; the  beam  is  held  by  two  bolts  in  the  top  angle  and  two  in 
the  seat  angle  unless  more  are  required  for  wind  bracing.  Such  con- 
nections, with  and  without  stiffening  angles,  are  shown  in  Fig.  133,  and 


90 


PART   II  —  STRUCTURAL  DRAFTING 


E  1,  Fig.  87,  is  a  typical  channel  supported  in  this  way.  The  beams 
for  these  types  of  connection  should  be  ordered  with  provision  for  the 
usual  overrun  (page  88  : 1)  and  for  easy  erection,  but  they  should  not 
be  ordered  so  short  that  the  whole  loads  rest  on  the  unsupported 
out-standing  legs  of  the  seat  angles;  unless  stiffening  angles  are  used 
the  ends  of  the  beams  should  extend  at  least  over  the  fillets  of  the  seat 
angles  and  preferably  over  part  of  the  vertical  legs.  Beams  -should 
be  ordered  to  the  nearest  half  inch  in  length. 

1.  Purlins.  —  The  beams  in  the  flat  roofs  of  office  buildings  are 
usually  similar  to  the  corresponding  floor  beams.    The  beams  may 
have  to  slope  to  give  the  roof  the  desired  pitch,  but  often  the  beams 
are  made  horizontal  and  a  slight  pitch  is  provided  by  varying  the 
thickness  at  the  beams  of  the  concrete  or  other  material  in  the  roof. 
Steep  roof  construction  such  as  used  in  mill  buildings  is  quite  different. 
The  roofing  is  supported  by  longitudinal  lines  of  "purlins  "  which  are 
connected  to  angles  on  the  top  chords  of  the  roof  trusses  or  rafters. 
The  type  and  the  spacing  of  the  purlins  depend  upon  the  style  of  the 
roofing  to  be  used  (page  114  :  2).     Typical  connections  for  different 
types  of   purlins   are   shown  with  dimensions  on  page    315;    web 
connections  are  provided  in  every  case,  but  the  flanges  of  only  the 
heavier  purlins  are  connected;    extra  holes  in  the  webs  are  used  when 
the  purlins  act  also  as  struts  (page  119  :  1).     Channel  purlins  are  used 
most  commonly,  usually  with  the  flanges  facing  up  the  slope.     Purlins 
are  usually  made  to  extend  over  two  bays  with  "broken  joints  "  in 
order  to  stiffen  the  structure,  i.e.,  the  joints  in  one  line  are  arranged 
to  come  at  different  trusses  from  the  joints  in  adjacent  lines,  as 
shown    in    the   diagram    on    page    156.      The  purlins  are  usually 
ordered  1"  shorter  than  the  distance  between  the  centers  of  the 
trusses,  thus  leaving  1"  clearance  between  the  ends.      For  typical 
purlin  details  see  Fig.  90. 

2.  Holes  should  be  provided  in  the  webs  of  beams  for  tie  rods  when 
rods  are  necessary  to  resist  the  thrust  of  floor  arches.     The  number 
and  the  size  of  the  rods  are  usually  determined  by  the  designing  de- 
partment; *  the  most  common  sizes  are  f "  and  f "  in  diameter.     The 
holes  are  usually  made  the  same  size  as  others  in  the  web  for  con- 

*  For  the  method  of  design,  see  page  201  :  3. 


DRAF" 
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PING  FORM  2 
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UNIVERSITY    BRIDGE    COMPANY 

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WING  CHECKED  BY            F.  F.  6.                              DATE       Feb.   19,    1918               SHEET  NUMBER    B     9 

Fig.  90.   Typical  Purlins. 


CHAPTER  XVII 


BEAMS 


91 


venicnce  in  punching  them;  they  are  made  in  pairs  (3"  apart)  to  provide 
for  the  rods  in  adjacent  panels  as  indicated  in  the  floor  plan  in  Fig. 
158.  The  location  of  the  holes  vertically  depends  upon  the  floor  con- 
struction because  the  rods  should  be  placed  where  they  will  best  serve 
their  purpose;  this  depends  upon  the  type  of  arch,  and  upon  whether 
the  arch  is  supported  by  the  top  or  bottom  flange  or  by  a  skewback 
angle  riveted  to  the  web  (Fig.  87).  On  account  of  the  use  of  dif- 
ferent depths  of  beams  in  the  same  floor,  the  elevation  of  the  rods  is 
usually  determined  at  the  outset  and  noted  on  the  plans,  as  shown  in 
Fig.  158. 

1.  Holes  should  be  provided  in  the  webs  of  purlins  for  sag  rods. 
The  function  of  the  sag  rods  is  to  give  intermediate  support  to  the 
purlins  at  right  angles  to  their  webs;    this  is  necessary  because  the 
resultant  forces  for  which  the  purlins  are  designed  are  not  parallel  to 
the  webs.     One  line  of  rods  is  used  if  the  span  between  trusses  is  from 
15  to  20  feet  and  two  lines  if  more  than  20  feet.     The  upper  purlins 
should  be  tied  to  each  other,  or  to  a  strut  at  the  ridge  by  means  of  bent 
rods  (Fig. 175  (6).     Rods  from  f"  to  f"  in  diameter  are  used  but  f"  is 
the  most  common  size.     The  holes  are  usually  made  the  same  size  as 
others  in  the  web  provided  they  are  small  enough  to  leave  sufficient 
bearing  for  the  nuts.     The  holes  are  made  in  pairs  (3"  apart),  either  in 
the  center  of  the  web  or  on  line  with  the  holes  for  the  truss  connections 
(see  next  paragraph). 

2.  When  a  multiple  beam  punch  is  to  be  used  all  the  rivets  and  holes 
in  the  web  of  an  I-beam  or  a  channel  should,  if  possible,  be  so  located 
that  the  beams  will  not  have  to  be  shifted  laterally  as  they  pass  through 
the  punch.     Holes  for  tie  rods,  sag  rods,  and  anchors  may  be  moved 
slightly  to  meet  this  requirement. 

3.  Wooden  floors  and  wooden  sheathing  are  attached  to  steel  beams 
or  purlins  by  means  of  wooden  nailing  strips  or  spiking  pieces  which  are 
bolted  to  the  steel.     The  nailing  strips  are  usually  bolted  to  the  webs 
of  channel  purlins  and  to  the  top  flanges  of  beams,  with  \"  bolts,     -fa" 
holes  must  be  provided  for  these  bolts  at  intervals  of  from  I'-O"  to 
l'-6",  preferably  in  multiples  of  3"  to  permit  the  use  of  standard  strip 
templets;    in  the  flanges  of  I-beams  the  holes  should  be  staggered.     It 
is  well  to  note  that  these  holes  are  "for  wood  "  so  that  shopmen  need 


not  waste  time  in  useless  refinements.  See  B  16,  Fig.  92,  and  P  6, 
Fig.  90.  Care  should  be  taken  to  space  the  holes  in  the  flanges  of 
beams  far  enough  from  the  ends  to  allow  for  any  underrun  or  any 
coping,  and  far  enough  from  the  connections  for  any  other  beams  which 
might  prevent  the  insertion  of  the  bolts. 

4.  Holes  in  the  flanges  of  I-beams  and  channels  may  sometimes  be 
dimensioned  in  the  front  and  the  end  views  in  order  to  dispense  with  the 
top  and  bottom  views,  as  hi  Figs.  90  and  92.     When  there  is  a  large 
number  of  holes,  or  when  the  drawing  might  be  misinterpreted,  the 
flange  views  should  be  shown;    for  example,   staggered  holes  should 
regularly  be  shown,  as  in  B  16,  Fig.  92. 

5.  Beam   Girders.  —  In  order  to  give  greater  strength  or  greater 
bearing,  two  I-beams  or  an  I-beam  and  a  channel  may  be  used  side  by 
side.     To  distribute  the  loads  and  make  them  act  as  a  single  member 
they  should  be  bolted  together  with  separators  of  some  form  between 
them.     Cast-iron  separators  are  commonly  used,  but  for  heavy  work, 
or  for  beams  of  unequal  depth,  special  diaphragms  made  of  I-beams, 
or  of  plates  and  angles,  are  used.     For  lighter  use,  gas-pipe  separators 
may  serve,  particularly  if  they  are  required  simply  for  holding  the  beams 
at  fixed  distances  apart.     Gas-pipe  separators  are  used  between  grillage 
beams  with  a  single  rod  passing  through  all  the  beams  of  one  tier.     (See 
Fig.  291).     Gas-pipe  and  cast-iron  separators  are  shown  on  page  316. 
They  are  not  drawn  in  detail,  but  are  simply  listed  on  combination 
shop   and   shipping  bills   (page   174  :  1).     The  separators  are   spaced 
about  four  or  five  feet  apart,  and  from  six  inches  to  one  foot  from  the 
ends.     If  the  beams  have  rigid  connections  at  the  ends,  the  end  sepa- 
rators may  be  omitted.     The  I-beams  and  the  separators  are  usually 
shipped  separately  and  assembled  in  the  field  (C  17,  Fig.  92),  but  this 
depends  upon  the  number  and  the  size  of  the  beams,  and  upon  the 
practice  of  the  individual  companies.     If  they  are  assembled  in  the 
shop  the  two  beams  should  be  detailed  together  and  called  a  girder,  as 
G  19,  Fig.  92;   a  list  of  separators  and  bolts  should  then  be  given  on 
the  drawing  and  on  the  corresponding  shop  bill;   on  the  latter,  reference 
should  be  made  to  the  shop  and  shipping  bills  from  which  the  separators 
and  bolts  are  made  and  these  bills  should  bear  the  note:   "Send  to  the 
shop  for  assembling." 


92 


PART   II  —  STRUCTURAL   DRAFTING 


DRAFTING  FORM  3 


UNIVERSITY   BRIDGE   COMPANY 


BRANCH 

..DRAWING  O 


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HOLES Hflci'!?f?ff  DRAWING  CHECKED  BY **•?•_* DATE_  jlffl'_®_W SHEET  NUMBER  B-?- 


DRAFTING  FORM  1 


STRUCTURE 


UNIVERSITY   BRIDGE  COMPANY 


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Fig.  92.   Typical  Beams. 


CHAPTER  XVII 


BEAMS 


93 


DRAFTING  FORM  4 


UNIVERSITY   BRIDGE  COMPANY 


STRUCTURE... 


_  .BRANCH 
DRAWING  0£._ 


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HOLES  jf"_J>RAWING  CHECKED  BY B.F.J, DATE-/;4'-'?^_-SH£ET  NUMBER    B./— 


DSAFTING  FORM  4 


STRUCTURE__ 


UNIVERSITY   BRIDGE   COMPANY 

_____________  BRANCH 

__DBAWING  QE  ______  Beam>_ 


RIVETS i DRAWING   MADE_BY •Li-^L DATE_7-^?rW-*_ _ CONTRACT-NO-.- 

HOLES__{rI.J)RAWING  CHECKED_B.Y__6f;.S. DATE- /i?:^ SH.EET  NUMBER 


Fig.  93.   Typical  Beams. 


94 


PART  II  —  STRUCTURAL  DRAFTING 


Special  forma  are  often  printed  for  double  I-beam  girders,  but  the  form  for  single 
I-beams  may  be  used  by  tracing  an  additional  I-beam  or  channel  in  the  end  views 
from  another  sheet,  as  in  G  19  and  G  20,  Fig.  92. 

1.  When  I-beam  girders  with  separators  are  insufficient,  plates  may 
be  added  to  make  a  box  sec  ion,  the  separators  being  omitted  as  in 
G  20,  Fig.  92.     The  rivets  are  spaced  6"  apart,  with  one  or  two  smaller 
spaces  near  the  ends.     Obviously,  rivets  through  the  inner  flanges  would 
be  inaccessible! 

2.  Wall  plates  or  flange  plates  are  sometimes  riveted  to   the  top 
flanges   of   beams  which  support  masonry  walls   in   order  to  furnish 
wider  bearing.     These  plates  are  not  necessarily  concentric  with  the 
beams. 

3.  Skewback  angles  are  sometimes  riveted  to  the  webs  of  beams  to 
provide   supports  for  floor  arches  at  the  proper  elevations.     Rivets 


should  be  spaced  about  I'-O"  apart,  as  shown  in  B  10  and  H  14,  Fig.  87. 
Similarly,  stiffening  angles  are  often  riveted  to  purlins  which  act  as 
struts,  as  shown  in  P  8,  Fig.  90,  and  S  2,  Fig.  147.  These  rivets  may 
be  spaced  l'-6"  apart. 

4.  Crane  runway  beams  are  sometimes  stiffened  laterally  by  chan- 
nels riveted  as  shown  in  G  24,  Fig.  93.     The  rivets  are  placed  at  inter- 
vals of  about  l'-6",  except  at  the  ends  where  about  two  3"  spaces  are 
used.     For  export  work  these  channels  and   the  I-beams 

should  be  shipped  separately. 

5.  For  skew  connections  see  page  146  :  5.     Note  that  it 

is  usually  better  to  cope  out  one  flange  of  a  beam  to  give        Fig.  94. 
desired  clearance,  as  in  Fig.  93,  than  to  require  a  diagonal 
cut  which  must  be  sawed.     Even  though  the  web  must  be  cut  diagonally, 
the  flanges  may  often  be  blocked  out  to  avoid  sawing,  as  in  Fig.  94. 


CHAPTER  XVIII 
PLATE   GIRDERS 

SYNOPSIS:  Specific  suggestions  for  drawing  typical  plate  girders. 


1.  Plate  girders  are  used  extensively  in  every  form  of  steel  construc- 
tion, because  of  their  adaptability.  They  resist  transverse  bending  like 
beams  (page  83  :  1),  but  they  are  used  for  heavier  loads,  for  longer 
spans,  or  for  conditions  which  the  single  rolled  beams  do  not  satisfy. 
With  different  depths,  different  forms  of  flanges,  or  different  sizes  of 
component  parts,  girders  may  be  made  to  serve  a  great  variety  of  purposes. 


Fig.  95.  Typical  Girder  Cross  Sections. 

2.  Types.  —  Girders  may  be  composed  of  one  or  more  web  plates,  with 
simple  or  composite  flanges,  as  illustrated  in  Fig.  95.  The  most  com- 
mon type  of  cross  section,  shown  at  (a)  and  (b),  is  composed  of  a  single 
web  plate  and  four  angles,  with  or  without  one  or  more  cover  plates  on 


95 


each  flange.  This  form  may  be  adapted  to  suit  most  requirements,  the 
heavier  types  of  flanges  being  used  only  in  special  cases.  Only  the  more 
common  girders  are  illustrated  in  this  chapter. 

3.  Main  Dimensions.  —  The  length  of  a  plate  girder  which  is  dimen- 
sioned on  the  drawing  is  usually  the  extreme  length  out  to  out;  when 
some  other  dimension  is  seemingly  more  important  it  may  be  given 
instead,  as  for  example  the  distance  from  center  to  center  of  end  holes 
when  the  end  connection  is  of  a  type  similar  to  the  alternate  form  shown 
in  the  corner  of  Fig.  99.  For  convenience  in  the  drafting  room  the 
distance  from  center  to  center  of  supports  is  usually  given  also,  as  in 
Figs.  98,  100,  or  103.  The  distance  from  the  end  of  the  girder  to  the 
center  of  the  support  should  provide  for  ample  clearance,  as  explained 
on  page  73  :  1.  The  nominal  depth  of  a  girder  is  usually  the  depth 
(width)  of  the  web  plate,  for  this  is  generally  in  even  inches  and  often  in 
even  feet  or  half  feet;  the  depth  dimensioned  upon  the  drawing  is  in- 
variably the  distance  from  back  to  back  of  flange  angles,  which  is  \" 
(or  i")  more  than  the  depth  of  the  web  plate.  The  flange  angles  thus 
project  beyond  the  edges  of  the  plate  to  allow  for  any  irregularities  in 
the  latter  which  may  result  from  rapid  shearing  in  the  mill  (page  25  :  3) ; 
if  part  of  the  plate  should  project  beyond  the  angles  it  would  have  to  be 
chipped  off  before  the  cover  plates  or  other  parts  could  be  put  in  proper 
position  against  the  angles.  Unless  the  upper  edge  of  the  plate  is  ex- 
posed to  the  weather,  the  depth  of  the  girder  from  back  to  back  of  flange 
angles  is  usually  made  \"  greater  than  the  depth  of  the  web  plate,  allow- 
ing \"  variation  on  each  edge.  In  bridge  and  viaduct  work  and  in  other 
structures  in  which  the  girders  are  exposed  to  the  elements,  the  upper 


96 


PART   II  —  STRUCTURAL   DRAFTING 


edges  of  the  web  plates  are  made  flush  with  the  backs  of  the  angles  unless 
cover  plates  are  used;  otherwise,  a  rain  pocket  is  formed  which  will  lead 
to  a  more  rapid  deterioration  of  the  girder.  The  distance  back  to  back 
of  angles  is  thus  j"  greater  than  the  depth  of  the  web  plate  for  exposed 
girders  without  cover  plates.  It  is  well  to  add  a  note  stating  whether  or 
not  any  projections  which  may  occur  should  be  chipped  off.  See  Figs. 
98  and  99.  It  is  not  feasible  to  draw  extra  lines  to  represent  the  edges 
of  the  web  plate,  the  only  indication  of  the  difference  in  depth  being  the 
discrepancy  between  the  billed  width  of  the  plate  (usually  in  even  inches, 
page  43  :  3)  and  the  dimension  back  to  back  of  angles  (usually  with  a 
fraction). 

1.  Since  the  vertical  shearing  stresses  of  a  plate  girder  are  resisted  by 
the  web  plate,  they  must  be  transmitted  from  the  web  to  the  supports. 
Sometimes  the  web  plate  is  riveted  directly  to  the  face  of  a  column  or 
to  the  stiffening  angles  of  another  girder  (Fig.  99) ;  but  more  often  end 
stiffeners  are  used  either  to  serve  as  connection  angles  (Figs.  98,  100 
or  104),  or  to  transmit  the  stresses  to  the  masonry  or  to  the  column  seat 
upon  which  the  girder  rests  (Figs.  101,  102,  or  105).     The  size  of  the 
end  stiffeners  and  the  number  of  rivets  in  them  are  determined  as  ex- 
plained in  Chapter  XXXIX,  page  266.     Stiffening  angles  should  be 
made  to  bear  against  the  outstanding  legs  of  the  flange  angles;  since  they 
are  placed  in  contact  with  the  vertical  legs  of  the  flange  angles,  they  must 
be  cut  to  fit  the  curved  fillets,  as  shown  in  Fig".  267  (6) .     The  billed  length 
of  the  stiffeners  is  the  exact  distance  in  the  clear  between  the  outstand- 
ing legs  of  the  flange  angles;  the  ordered  length  is  made  \"  greater  (see 
next  paragraph).     For  suggestions  regarding  the  spacing  of  the  rivets 
see  page  70  :  4  (6).     The  spacing  should  ordinarily  be  made  symmetrical 
about  the  center  line,  so  that  the  stiffeners  on  opposite  sides  of  the  web 
are  interchangeable;  but  if  the  holes  for  a  connection  to  the  outstanding 
legs  are  necessarily  slightly  unsymmetrical,  it  may  be  deemed  advisable 
to  space  at  least  one  rivet  through  the  web  unsymmetrically  to  prevent 
the  possibility  of  the  stiffeners  being  assembled  upside  down. 

2.  The  flange  angles  usually  extend  the  full  length  of  a  girder  and 
should  be  billed  accordingly.     They  are  ordered  about  f"  long  and  are 
then  cut  to  the  required  length  in  the  shop  where  they  can  be  cut  with 
greater  precision  than  at  the  mill  (page  28  :  1).     The  stringers  and  floor 


beams  of  bridges  are  often  milled  at  the  ends;  otherwise  the  angles  are 
sheared.  The  extra  f  "  is  indicated  on  the  material  order  bills  and  on  the 
shop  bills  (pages  165  :  1  and  167  :  4).  Web  plates  should  extend  to  the 
extreme  ends  of  a  girder  when  they  are  to  be  milled  or  when  no  stiffeners 
are  placed  with  their  outstanding  legs  at  the  extreme  ends  of  the 
girder;  when  stiffening  angles  are  so  placed  the  web  plates  may  be  billed 
long  enough  to  come  within  \"  or  f"  of  each  end.  In  the  larger  girders 
the  web  plates  must  be  spliced  because  it  is  impossible  to  obtain  plates 
long  enough  to  extend  the  full  length  of  the  girder.  For  the  location 
and  the  design  of  web  splices  see  page  270  :  4.  The  lengths  of  the  web 
sections  should  be  billed  to  allow  from  \"  to  f"  between  them  at  the 
splices  (compare  page  165  :  2). 

3.  Unless  the  web  plate  of  a  girder  is  thick  enough  to  resist  the  shear- 
ing stresses,  it  must  be  reinforced  by  intermediate  stiffening  angles,  as 
explained  on  page  266  :  2.     When  the  position  of  stiffening  angles  is 
definitely  determined  by  members  which  are  to  connect  to  the  outstand- 
ing legs,  the  stiffeners  must  be  spaced  before  the  flange  rivets;  otherwise 
it  is  better  to  fix  the  flange  rivet  spacing  first,  and  then  place  the  stiffeners 
at  those  rivets  which  are  located  most  suitably  to  give  the  best  spacing 
(page  269  :  3).     It  is  customary  to  place  the  stiffeners  so  that  the  backs 
of  the  angles  are  toward  the  nearer  end  of  a  girder.     The  rivets  in  the 
intermediate  stiffeners  should  line  up  with  those  in  the  end  stiffeners  even 
when  a  smaller  number  is  used;    this  saves  extra  dimensioning,  and  it 
simplifies  the  shop  work,  particularly  when  multiple  punches  are  used 
(page  29  :  5).     Instead  of  using  the  full  number  of  rivets  used  in  the  end 
stiffeners,  some  may  be  omitted  unless  the  resulting  spaces  exceed  th{ 
allowed  maximum  (page  69  :  1),  or  unless  the  full  number  of  rivets  h 
needed  for  other  reasons  (as  for  example,  when  the  stiffeners  serve  a.1 
connection  angles  for  other  members  or  when  they  are  placed  at  we! 
splices). 

4.  Stiffening  angles  overlap  the  vertical  legs  of  the  flange  angles,  anc 
unless  they  are  crimped  (see  next  paragraph)  spaces  are  left  between  th< 
stiffeners  and  the  web  as  shown  in  Fig.  97.     Plates  called  "  fillers  "  ari 
inserted  to  "fill  "  these  spaces  so  that  the  rivets  can  be  effectively  drivei 
without  bending  the  angles  out  of  line,  and  so  that  no  surfaces  will  be  lef 
inaccessible  for  painting.     The  width  of  a  filler  should  be  the  same  a 


CHAPTER  XVIII 


PLATE   GIRDERS 


97 


the  width  of  the  superimposed  stiffening  angle  unless  the  filler  is  made  to 
extend  under  two  or  more  angles,  or  made  wide  enough  to  take  an  addi- 
tional row  of  rivets  according  to  page  235  :  2.  The  thickness  of  the  filler 
should  be  the  same  as  the  thickness  of  the  flange  angles,  unless  part  of 
this  space  is  occupied  by  a  splice  plate  or  a  reinforcing  plate.  In  this 
case  the  filler  should  be  thick  enough  to  make  up  the  difference;  fillers 
less  than  f\"  are  not  used,  and  smaller  differences  should  be  made  up  by 
making  the  thickness  of  the  splice  plates  or  reinforcing  plates  equal  to 
that  of  the  flange  angles.  If  the  thicknesses  of  the  top  and 
bottom  flange  angles  differ  by  11ff"  tne  fiUer  maY  be  made  of 
either  thickness.  If  they  differ  by  5"  the  filler  may  usually  be 
made  the  mean  thickness.  If  they  differ  by  more  than  |"  two 
fillers  should  be  used,  one  as  thick  as  the  thinner  angle  and  the 
other  equal  to  the  difference  in  thickness;  this  second  filler 
should  extend  to  the  fillet  of  the  thinner  angle.  The  length 
of  the  filler  should  preferably  be  made  about  \"  less  than  the 
clear  distance  between  the  flange  angles,  allowing  the  usual 
shop  clearance  of  \"  at  each  end.  On  girders  which  are  ex- 
posed to  the  weather  it  is  well  to  reduce  this  clearance  one- 
half  to  leave  less  chance  for  water  to  enter,  but  due  allowance 
should  be  made  for  the  overrun  of  heavy  angles  (page  25  : 1). 
Some  specifications  require  the  fillers  under  end  stiffeners  to 
fit  tightly  at  the  bottom. 

1.  Intermediate  stiffening  angles  are  sometimes  "crimped  "  or  bent  so 
that  they  are  brought  into  contact  with  the  web,  as  shown  in  Section  BB, 
Fig.  102.  No  fillers  are  required  under  crimped  stiffeners.  Stiffeners 
which  transmit  direct  stress  should  not  be  crimped  because  straight 
angles  are  more  effective;  thus  end  stiffeners  or  stiffeners  under  con- 
centrated loads  should  not  be  crimped.  Similarly  stiffeners  which  have 
holes  in  the  outstanding  legs  for  the  connection  of  other  members  should 
always  rest  upon  fillers,  because  better  results  can  be  obtained  in  this 
way.  Most  specifications  permit  the  crimping  of  all  other  intermediate 
stiffeners  although  not  all  companies  are  well  equipped  for  this  work. 
Many  companies  prefer  to  furnish  fillers,  particularly  when  the  cost  of 
the  additional  material  is  met  by  the  customer,  as  in  contracts  based 
upon  a  price  per  pound.  The  billed  length  of  a  crimped  stiffening  angle 


Fig.  97. 


should  include  the  amount  of  metal  required  for  each  crimp,  which  is 
equal  to  the  depth  of  the  crimp,  i.e.,  the  thickness  of  the  flange  angle. 
Thus  the  length  of  a  crimped  stiffener  of  a  girder  is  equivalent  to  the 
depth  of  the  girder  from  back  to  back  of  flange  angles.  An  extra  \" 
should  be  ordered  for  each  crimp,  so  that  the  angles  can  be  cut  to  fit 
properly  after  they  are  bent. 

2.  Cover  plates  may  be  used  on  plate  girders  to  furnish  additional 
metal  in  the  flanges.  Since  the  flange  stress  is  a  function  of  the  bending 
moment,  the  greatest  flange  area  is  required  where  the  moment  is  maxi- 
mum; as  the  moment  decreases,  the  flange  area  may  be  reduced.  This 
reduction  is  effected  by  cutting  off  the  cover  plates  successively  at  points 
beyond  which  they  are  no  longer  needed,  as  explained  in  Chapter 
XXXVIII,  page  259.  If  a  girder  is  to  be  exposed  to  the  weather, 
one  plate  on  the  top  flange  and  sometimes  one  on  the  bottom  flange 
are  made  to  extend  the  full  length  of  the  girder  in  order  to  protect  the 
surfaces  of  contact  between  the  angles  and  the  web  from  the  action  of 
the  elements.  Similarly,  all  the  cover  plates  on  the  top  flanges  of  crane 
runway  girders  must  be  continuous  in  order  to  furnish  uniform  bearing 
for  the  rails  which  rest  directly  upon  them.  The  cover  plates  on  the 
top  flange  of  a  railway  deck  girder  need  not  necessarily  be  made  full 
length,  since  the  ties  may  be  "dapped  "  (i.e.  notched),  different  amounts 
to  make  up  for  the  differences  in  plate  thickness;  the  ties  must  be  notched, 
also,  for  the  rivet  heads.  Special  detailed  drawings  are  often  prepared 
in  the  drafting  room  for  the  ties  of  a  bridge,  especially  when  they  have 
to  be  sawed  to  provide  for  the  super-elevation  of  the  outer  rail  on  a 
curve.  The  cover  plates  may  be  billed  with  the  flange  angles  (Fig. 
105),  or  they  may  be  billed  on  special  dimension  lines  with  the  dis- 
tance from  the  end  of  each  plate  to  the  end  of  the  girder,  as  shown 
in  Fig.  101.  To  save  space,  all  the  plates  of  one  flange  may  be  billed 
as  in  Fig.  102,  provided  portions  of  the  line  are  omitted  so  that  the 
overlapping  dimensions  may  be  distinguished  more  easily.  Universal 
Mill  plates  with  rolled  edges  are  usually  ordered  for  cover  plates,  par- 
ticularly for  girders  which  are  exposed  to  the  weather  (page  25:3). 
Full  length  plates  are  ordered  f "  long  the  same  as  the  flange  angles 
(page  96  :  2) ;  other  plates  are  ordered  the  same  as  the  billed 
lengths. 


PART  II  —  STRUCTURAL  DRAFTING 


rrf                                                                                              I4*0"c.  tO  C. 

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N.Y.N.H.S(H.R.R. 
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UNIVERSITY  BRIDGE  COMPANY 

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Fig.  98.   Railroad  Bridge  Stringer. 


CHAPTER  XVIII 


PLATE  GIRDERS 


99 


s; 

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ALTERNATE  FORM  OF  CONNECTION 


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THRU.  PLATE  GIRDER  BRIDGE 

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NEW  HAVEN,  CONN. 

UNIVERSITY  BRIDGE  COMPANY 


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1900 


Fig.  99.  Floor  Beams  for  Through  Railroad  Girder  Bridge. 


100 


PART   II  —  STRUCTURAL  DRAFTING 


Web  flush  top  (may  project's} 


Web  67  x is*  9-1  If" 


2  L 


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FLOOR  BEAMS 
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UNIVERSITY  BRIDGE  COMPANY 


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Fig.  100.   Floor  Beam  for  Pin-connected  Truss  Bridge. 


CHAPTER  XVIII 


PLATE  GIRDERS 


101 


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UNIVERSITY  BRIDGE  COMPANY 

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Fig.  101.   Through  Railroad  Bridge  Girder. 


102 


PART   II  —  STRUCTURAL   DRAFTING 


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Fig.  102.   Deck  Railroad  Bridge  Girder. 


CHAPTER  XVIII 


PLATE  GIRDERS 


103 


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104 


PART  II  —  STRUCTURAL  DRAFTING 


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CHAPTER  XVIII 


PLATE   GIRDERS 


105 


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FOUNDATION  GIRDERS 
POWER  HOUSE 
LIGHT  AND  POWER  CO. 

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UNIVERSITY  BRIDGE  COMPANY 

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Fig.  105.   Box  Girder. 


106 


PART  II  —  STRUCTURAL   DRAFTING 


1.  Flange  Rivets.  —  The  flange  angles  of  a  girder  are  fastened   to 
the  web  plate  by  sufficient  rivets  to  transmit  the  flange  stress  for  which 
the  angles  are  designed.     The  rivets  are  usually  closer  together  toward 
the  ends  of  a  girder  than  they  are  near  the  center.     The  pitch  for  each 
section  of  a  girder  must  be  determined  for  the  conditions  of  loading  and 
the  proportions  which  are  peculiar  to  that  girder.     The  maximum  pitch 
for  each  panel  is  found  as  explained  under  the  proper  case  in  Chapter 
XXXVII,  page  241.     The  minimum  pitch  depends  upon  the  strength 
of  the  web,  as  explained  on  page  255 : 2.     Between  these  limits  the  drafts- 
man should  space  the  rivets  according  to  the  general  rules  for  rivet 
spacing  given  in  Chapter  XIII,  particularly  pages  69  :  1,  70 :  2,  and 
70  :  4;   the  spacing  of    the   rivets  should  be  made  the  same  in  both 
flanges  for  the  benefit  of  the  draftsman  and  the  shopmen. 

2.  Rivets  in  Cover  Plates.  —  The  rivets  which   fasten   the   cover 
plates  to  the  flange  angles  must  satisfy  the  conditions  given  on  page 
263  :  3,  but  except  in  heavy  or  unusual  work,  the  spacing  is  governed 
by  the  general  rules  for  rivet  spacing  given  in  Chapter  XIII,  page 
68.     A  single  line  of  rivets  is  often  used  in  each  5"  or  6"  angle  even 
if  a  double  line  is  used  in  the  vertical  leg.     Extra  rivet  lines  are  placed 
in  wide  cover  plates,  as  explained  on  page  69  :  2.     Holes  for  lateral  brac- 
ing should  be  spaced  before  the  stiffening  angles  are  located  for  usually 
the  angles  can  be  so  placed  that  their  outstanding  legs  will  not  interfere 
with  the  holes  which  best  meet  the  requirements  of  the  lateral  plates. 
The  flange  rivets  and  the  stiffening  angles  should  usually  be  spaced  before 
the  remaining  rivets  in  the  cover  plates.     No  rivets  in  the  cover  plates 
should  be  placed  so  near  the  outstanding  legs  of  the  stiffening  angles 
that  they  cannot  be  driven  by  machine  (page  73  :  5) ;  it  is  well,  there- 
fore, to  tie  the  nearest  rivet  through  the  cover  plate  to  the  rivet  line  of 
each  pair  of  stiffeners  by  a  line  or  a  dimension,  as  in  Fig.  102,  in  order 
to  show  that  this  point  has  not  been  overlooked.     The  rivets  in  the 
plates  should  be  so  placed  that  the  same  templets  can  be  used  for  the 
top  plates  and  angles  that  are  used  for  the  bottom  plates  and  angles; 
additional  rivets  or  groups  of  rivets  may  be  spaced  differently  to  accom- 
modate connecting  members,  but  the  remaining  rivets  should  be  oppo- 
site (see  (d),  page    70:2).     The  rivets    near   the  end  of  each  cover, 
plate  should  be  spaced  not  over  four  diameters  as  explained  in  (d), 


page  69  :  1 ;  this  applies  to  plates  on  the  tension  flanges  as  well  as  those 
on  the  compression  flange  so  that  the  strength  of  the  plates  may  be 
developed  within  a  comparatively  short  distance.  Since  all  cover  plates 
which  do  not  extend  full  length  of  the  girder  should  be  used  as  ordered, 
the  end  rivets  should  be  placed  If"  from  the  ends  of  the  plates  to  provide 
ample  edge  distance  in  case  the  plates  underrun  (page  165  :  2). 

3.  Standard  gages  are  not  necessarily  used  in  the  outstanding  legs 
of  the  flange  angles  or  of  the  stiffening  angles.     It  is  usually  preferable 
to  change  the  gage  sufficiently  to  make  the  distance  from  center  to 
center  of  rows  a  multiple  of  5",  and  the  distance  from  the  center  of  the 
web.  to  either  row  a  multiple  of  j" ;  in  this  way  small  fractions  are  used 
in  the  gages  only,  and  are  avoided  in  the  cover  plates  and  on  the  draw- 
ings of  members  which  connect  to  the  flanges  or  to  the  stiffeners.     In 
order  to  eliminate  thirty  seconds  from  the  gages,  web  thicknesses  in 
sixteenths  should  be  considered  ^V"  greater;    this  incidentally  allows 
for  paint,  scale,  or  bends  which  might  tend  to  separate  the  surfaces  of 
contact. 

4.  When  the  outstanding  legs  of  two  stiffening  angles  are  in  contact 
they  need  not  as  a  rule  be  riveted  together.     On  girders  which  are 
exposed  to  the  weather  these  outstanding  legs  should  be  riveted  at 
intervals  of  1'  0"  if  the  girders  are  3'  0"   or  more  in  depth.     It  is  pref- 
erable where  possible  to  place  such  stiffeners  at  least  2"  apart  so  that 
they  can  be  painted. 

5.  Holes  for  anchor  bolts  should  be  ^g"  or  f"  larger  than  the  bolts 
(Fig.  102);    this  facilitates  the  placing  of  a  girder  if  the  anchor  bolts 
have  been  set,  and  it  provides  for  drilling  holes  in  the  masonry  if  the 
bolts  are  to  be  placed  after  the  girder  is  in  position.     The  holes  at  one 
end  should  be  slotted  to  allow  for  expansion  and  also  for  inaccuracies 
in  setting  the  bolts.     Provision  for  expansion  to  the  extent  of  \"  for 
each   10'  0"  should   be  made  in  all   bridge   girders.     When   cast-iron 
pedestals  are  used  (see  diagram,  Fig.  153)  the  holes  in  the  girder  are 
made  only  the  usual  TV"  larger  than  the  bolts,  but  at  one  end  the  holes 
should  be  slotted  (Fig.  101). 

6.  Reference  dimensions  are  often  given  on  the  drawings  for  use  in 
the  drafting  room;  for  example,  dimensions  to  the  base  of  rail  (Fig.  100), 
or  to  the  floor  line  (Fig.  104) . 


CHAPTER  XVIII 


PLATE   GIRDERS 


107 


1.  When  more  than  one  sheet  must  be  used  to  properly  illustrate  a 
long  girder  a  reference  line  should  be  used  on  each  sheet  to  indicate  the 
points  which  are  common  to  both  drawings,  as  illustrated  in  Fig.  101 
(compare  page  121  :  2). 

2.  A  box  girder  with  more  than  one  web  is  shown  in  Fig.  105. 

3.  A  girder  is  sometimes  "  cambered,"  i.e.,  curved  in  a  vertical  plane, 
to  prevent  the  center  from  sagging  lower  than  the  ends.     The  amount 
of  camber  should  equal  the  maximum  deflection  so  that  the  girder  will 
assume  a  horizontal  position  under  a  full  load.     The  camber  is  effected 
partly  by  the  proper  rivet  spacing,  but  mostly  by  careful  shop  work; 
in  fact,  slight  cambers  may  be  made  entirely  by  the  fitters  and  riveters 
by  placing  the  proper  supports  under  the  girders  while  assembling  and 
riveting  them.     Since  a  web  plate  cannot  be  curved  except  by  elaborate 
cutting,  the  usual  camber  is  provided  at  the  web  splices  by  spacing  the 
rows  of  rivets  in  the  splice  plates  farther  apart  at  the  top  than  at  the 
bottom  so  as  to  separate  the  ends  of  the  adjacent  web  sections  more  at 
the  top.     The  corresponding  spaces  in  the  top  flange  angles  are  made 
greater  than  those  in  the  bottom  angles.     It  is  important  to  note  the 


amount  of  camber  on  the  drawing  even  if  special  rivet  spacing  is  pro- 
vided, for  it  is  as  easy  to  nullify  the  effects  of  such  spacing  by  careless 
fitting  up  or  riveting  as  it  is  difficult  to  avoid  a  curve  in  a  girder  which 
is  intended  to  be  straight. 

4.  Bridge  girders  are  often  made  with  curved  ends  for  the  sake  of 
appearance,  as  illustrated  in  Fig.  101.     It  is  not  feasible  to  bend  both 
ends  of  long  flange  angles,  so  short  angles  are  used  at  each  end.     These 
angles  extend  far  enough  horizontally  so  that  they  may  be  spliced  to 
the  top  flange  angles  satisfactorily.     They  serve  as  end  stiffeners,  and 
they  may  be  crimped  over  the  bottom  flange  angles  or  arranged  as  shown. 

5.  Typical  drawings  of  plate  girders  are  illustrated  as  follows:  —  Figs. 
98  and  99  ,  a  stringer   and  a  floor  beam  for  the  same    railroad  girder 
bridge;  Fig.  100,  a  floor  beam  for  a  truss  bridge,  showing  the  method  of 
cutting  the  end  to   clear  the   pin;    Figs.   101  and  102,  railroad  bridge 
girders;   Fig.   103,  a  crane  girder  with  holes  in  the  top  flange  for  rail- 
clamp  bolts  and  for  lattice  bars  which  connect  to  the  stiffening  girder  of 
Fig.  110;  Fig.  104,  a  floor  girder  with  beam  connections;  and  Fig.   105, 
a  box  girder  with  two  webs. 


CHAPTER  XIX 
LATTICED   GIRDERS 

SYNOPSIS:    Latticed  girders  are  light  trusses  with  parallel  chords,  but  a  different 
system  of  working  lines  is  used  from  that  of  the  next  two  chapters. 


1.  Definition.  —  The  terms  "latticed  girder"  and  "latticed  truss" 
are  not  distinctive  because  they  are  used  interchangeably  by  some 
companies  or  individuals  whereas  they  have  different  meanings  when 
used  by  others.     A  girder  becomes  a  latticed  girder  when  the  solid  web 
is  replaced  by  separate  web  members,  but  it  also  becomes  a  truss  from 
the  definition   (page  17).      Formerly,  a  latticed  truss  was  of  a  form 
similar  to  that  shown  in  Fig.  120  (h)  which  had  from  two  to  four  inde- 
pendent web  systems,  the  stresses  of  which  were  statically  indeterminate. 
Since  this  type  of  truss  is  becoming  obsolete  except  for  very  light  work 
(Fig.  Ill),  the  name  "latticed  truss"  is  often  used  to  apply  to  almost 
any  form  of  riveted  truss  with  parallel  chords  to  distinguish  it  from  a  pin- 
connected  truss.     In  this  book  the  term  "  latticed  girder  "  will  be  con- 
fined to  comparatively  light  trusses  with  parallel  chords,  all  members  of 
which  are  composed  of  one  or  two  angles.     Heavier  forms  will  be  called 
trusses,  and  to  avoid  ambiguity  the  term  "latticed  truss  "  will  not  be 
used;    it  will  be  replaced  by  the  more  specific  terms  "Pratt  truss," 
"Howe  truss,"  etc.,  as  illustrated  in  Chapter  XXI,  page  120. 

2.  The  most  common  form  of  latticed  girder  is  the  "Warren  "  or 
"triangular,"   shown   in   Fig.    120.     Some   authorities   limit   the   term 
"Warren  "  to  girders  formed  of  equilateral  triangles,  but  this  distinction 
is  not  generally  maintained.     In  order  to  increase  the  number  of  panels, 
or  to  provide  connections  for  other  members,  every  triangle  may  be 
subdivided   as   in    Fig.  120  (fc),   alternate  panels  may  be  subdivided 
as  in  Fig.  120  (m)  and  (n),  or  single  panels  may  be  subdivided  as  in 
Fig.  110. 


3.  End  Connections.  —  The  greatest  number  of  latticed  girders  are 
used  in  building  construction  where  they  are  supported  by  columns  or 
other  members.     Typical  column  connections  are  shown  in  Figs.  110  and 
111,  the  former  to  the  face  of  a  column  perpendicular  to  the  plane  of  the 
girder  and  the  latter  to  the  face  parallel  to  this  plane.     Note  that  in  the 
type  of  connection  shown  in  Fig.  Ill,  one  angle  of  each  chord  must  be 
cut  short  to  avoid  interference  with  the  column.     Small  foot  bridges  are 
often  supported  by  latticed  girders  which  rest  upon  the  abutments,  with 
shoe  plates  similar  to  those  used  on  plate  girders. 

4.  Proportions.  —  The  depth  of  a  latticed  girder  is  determined  in  the 
designing  department,  and  it  is  usually  expressed  in  even  half  feet.     In 
building  work  the  depth  is  often  dependent  upon  other  framing  because 
the  position  of  both  the  top  and  the  bottom  may  be  fixed  by  other  mem- 
bers.    The  panel  lengths  are  made  equal  in  the  drafting  room,  but  seldom 
are  the  resulting  triangles  equilateral  (see  above). 

5.  In  general  the  different  members  of  a  truss  are  referred  to  a  system 
of  working  lines.     Theoretically  these  working  lines  should  pass  through 
the  centers  of  gravity  of  the  different  members,  but  when  a  member  is 
composed  of  one  or  two  angles  it  is  customary  to  use  the  rivet  lines  as 
working  lines.     These  working  lines  should  intersect  in  a  common  point 
at  each  apex  as  in  roof  trusses  (Chapter  XX,  page    113)  and  bridge 
trusses   (Chapter  XXI,  page  120);    the  stresses  are  determined  upon 
this  assumption.     In  the  case  of  light  latticed  girders,  however,  the 
stresses  are  usually  so  small  that  a  slight  deviation  makes  practically  no 
difference  in  the  efficiency  of  the  girders,  and  better  connections  are  th 


108 


1US 


CHAPTER  XIX 


LATTICED   GIRDERS 


109 


obtained.  The  rivet  linos  of  the  diagonals  are  not  extended  to  the  rivet 
lines  of  the  chords  but  they  intersect  parallel  auxiliary  working  lines; 
the  end  rivets  of  the  diagonals  are  placed  at  these  intersections,  as  shown 
in  Fig.  110.  The  position  of  these  auxiliary  working  lines  should  be 
such  that  ample  clearance  is  left  between  the  angles  of  the  diagonals  and 
the  chord  angles,  as  explained  in  detail  on  page  77  :  1. 

1.  By  means  of  the  dimensions  determined  in  step  IV  (page  77  :  1) 
may  be  found  the  panel  depth  and  the  panel  length,  each  measured  from 
center  to  center  of  the  end  rivets  of  a  single  diagonal.  The  panel  length 
is  found  by  deducting  from  the  extreme  length  of  the  girder  the  sum  of 
the  distances  from  the  ends  to  the  first  working  points  and  the  distances 
between  the  working  points  in  each  intermediate  plate,  and  then  dividing 
the  remainder  by  the  number  of  diagonals.  This  resulting  panel  length 
is  expressed  to  the  nearest  sixteenth  inch,  or  preferably  the  nearest  eighth 
or  quarter,  the  amount  of  clearance  at  two  or  more  points  being  changed 
slightly  if  necessary  to  make  the  proper  adjustment.  Care  should  be 
taken,  however,  to  keep  all  panel  lengths  equal,  and  all  plates  alike,  as 
far  as  possible,  in  order  to  minimize  the  number  of  different  templets. 
For  illustration,  let  us  determine  the  panel  dimensions  for  the  girder 
shown  in  Fig.  110.  The  diagonal  distance  from  the  end  rivet  to  the 
farther  corner  of  any  diagonal  is  found  by  means  of  the  diagram  on 
page  313  to  be  2-,V'  for  a  If"  gage  and  1§"  edge  distance.  The 
distance  from  the  end  rivet  to  the  rivet  line  of  the  upper  chord  angles  is 
4-rV"  =  2A  +  j  +  3£  -  2,  allowing  £"  clearance  (page  72  :  2) ;  to 
eliminate  sixteenths  4"  is  used.  The  corresponding  distance  at  the 
bottom  is  made  the  same  in  order  to  keep  the  intermediate  plates  alike. 
The  panel  depth  from  center  to  center  of  working  lines  is  7'-6"  = 
8'-6"  -  2  (4  +  2).  The  distance  in  the  intermediate  plates  between 
the  end  rivets  of  adjacent  diagonals  is  4f  "  =  2^  •+•  i  +  2T5^.  Unless  it 
is  desired  to  make  provision  for  assembling  the  diagonals  with  the  out- 
standing legs  on  either  the  upper  or  lower  edges,  advantage  may  be  taken 
of  the  fact  that  there  is  no  plate  similar  to  the  end  plate  or  the  center 
plate;  at  each  of  these  points  the  diagonals  are  so  arranged  that  space 
need  be  provided  only  for  the  corners  nearer  the  end  rivets.  The  diag- 
onal distance  from  the  end  rivet  to  the  nearer  corner  is  found  from  the 
diagram  to  be  1||"  for  \\  (leg  minus  gage)  and  1^.  The  distance  from 


the  end  of  the  girder  to  the  first  working  point  is  5j£"  =  \\$  +  j  +  3^. 
From  the  center  line  to  the  nearest  working  point  is  5J"  =  1||  +  i  + 
3|  +  T3?-  Considering  one-half  of  the  symmetrical  girder,  the  amount 
to  be  divided  into  four  equal  panels  is  17'-9A"  =  2  (39'-10f")  - 
5H  —  3  X  4f  —  5f.  This  is  not  divisible  by  four  within  the  usual 
working  limits,  but  to  the  nearest  \"  we  can  use  4  panels  of  4'-5$"  = 
17'-9";  this  leaves  TV'  to  be  distributed  among  the  other  dimensions 
in  order  to  make  the  total  length  check  with  the  overall  dimension.  Each 
of  the  three  4|"  dimensions  could  be  increased  by  -fa";  but  it  would  be 
preferable  to  avoid  sixteenths,  and  consequently  the  5{£"  is  increased  to 
5f "  and  the  5|"  to  6",  as  shown. 

2.  The  dimensions  should  be  recorded  on  the  drawing  as  soon  as 
determined.     When  the  panel  depth  and  length  are  found  they  may  be 
laid  out  and  dimensioned,  and  the  angles  may  be  drawn  and  billed; 
the  gages  should  be  dimensioned  on  each  angle  though  the  standard 
gage  is  used. 

3.  The  sizes  of   the   connection  plates   may  be  determined   either 
graphically  or  arithmetically  as  explained    on    page    77  :  1,   V.     The 
experienced  draftsman  usually  prefers  the  second  method,  particularly 
for  rectangular  plates.     The  size  of  the  plate  will  generally  be  deter- 
mined by  the  rivets  in   the  diagonals,   and  afterwards  the  remaining 
rivets  may  be  spaced.     To  illustrate,  let  us  find  the  size  of  the  plate  pa, 
Fig.  110.     On  the  main  drawing  along  the  working  line  of  one  of  the 
diagonals  already  plotted  to  scale,  a  distance  is  laid  off  equal  to  the  sum 
of  the  rivet  spaces,  6"  =  3  +  3,  from  the  end  rivet  to  the  last  rivet  in 
the  group.     A  scale  of  3"  =  1'  should  be  used,  or  else  the  lines  should 
be  prolonged  so  that  a  full  size  scale  may  be  used.     The  corresponding 
vertical  and  horizontal  components  may  be  scaled  without  drawing  any 
additional  lines.     In  the  case  at  hand,  the  vertical  component  is  5j" 
and   the  horizontal   component  is  3^".     By   combining   these  values 
with  the  edge  distances  and  the  proper  distances  from  the  second  para- 
graph preceding,   the  dimensions  of  the  plate  are  found.     Thus,  the 
width  of  the  plate  with  l£"  edge  distances  would  be  12j"  =  Ij  +  4  + 
5|  +  H;  by  reducing  each  edge  distance  to  1TV,  the  commercial  width 
of  12"  may  be  used  (see  page  43  : 3).     The  length  of  the  plate  is  l'-2"  = 
lj  +  3TV  +  4|  +  3TV  +  H-     The    remaining    rivets   in    the    plate    are 


110 


PART   II  —  STRUCTURAL   DRAFTING 


2  Ls  5  x  3^x^x39- 


\    /  \    /  \  \/  \   /  \    /\/y/\/\    /\/\ 

—  6  holes  for  woiHl  mrk  ^ 

RIVETS  4 


I  GIRDER  LGI 
I  BRACKET  MI8 


LA  TT'ICED  GIRDER 

FURNACE  BUILDING 

NEW  ENGLAND  STEEL  CO. 

HARTFORD  CONN. 

^^-  UNIVERSITY  BRIDGE  COMPANY 

Yale  PLANT 


HOLES-ft  Oniass  noted 
WASHERS  2i*j- 


[N  CHARGE  OF. 


R.C. 


L.T.C.  7-30-14 


-14          p 
-14  *J 


56/3 


Fig.  110.  Typical  Latticed  Girder. 


CHAPTER  XIX 


LATTICED  GIRDERS 


111 


\IPI.I2xfjxl-2" 


IL4*3*%x39'-9j" 
I  L4x3xJ-  x  39-24" 


Sym.  abt,  C.Lexc;  taihewn 


2  LA  TT/CED  GIRDERS  LG  2 


I  L4x3x£-  x  39L21i 


Rivett 


LATTICED  GIRDERS 

POWER  HOUSE 

PORTSMOUTH  STEEL  CO. 

PORTS  MOUTH.  0. 

UNIVERSITY  BRIDGE  COMPANY 

PLANT 

IN  CHARGE  OF     T.  C,  *       2524 

MADE  Bv._a  M.9/2M4. 

CH'K'D  BY__W._0;j 


10 


Fig.  111.  Double  Latticed  Girder. 


112 


PART  II  —  STRUCTURAL  DRAFTING 


located  with  reference  to  the  working  points  of  the  diagonals  with  due 
consideration  to  the  edge  distances  and  the  maximum  spaces  allowed 
(page  69  :  1).  For  the  sake  of  appearance  the  plate  should  be  cut  so 
that  it  is  no  shorter  along  the  chord  angles  than  elsewhere.  In  the 
plate  referred  to  it  is  convenient  to  place  two  rivets  directly  below  the 
end  rivets  of  the  diagonals  in  order  to  save  additional  dimensions.  The 
remaining  spaces  are  expressed  to  the  nearest  \"  so  that  the  edge  dis- 
tances will  be  approximately  1^  (in  this  case  1-fV). 

1.  When  adjacent  diagonals  have  different  "numbers  of  rivets,  the 
connecting  plate  may  be  cut  diagonally,  or  else  the  smaller  number  of 
rivets  may  be  spread  so  that  the  resulting  edge  distances  will  not  be 
excessive.     Diagonal  cuts  should  preferably  extend  the  full  width'  of 
the  plate  in  order  to  save  waste;    in  this  case  the  width  of  the  plate 
should  be  the  perpendicular  distance  between  the  parallel  sides  even 
though  this  is  the  longer  dimension.     For  other  suggestions  regarding 
the  shape  of  plates  see  page  76  :  1,  IX. 

2.  The  size  of  the  end  connection  plates  may  be  governed  either  by 
the  rivets  in  the  diagonal,  or  by  the  number  of  field  rivets  required, 
whether  connection  angles  are  used  or  not.     Compare  Figs.  110  and  111. 
In  general,  the  rivets  along  the  chords  and  along  the  supporting  mem- 
bers should  be  so  spaced  that  the  full  width  and  length  of  the  plate 
are  used;    that  is,  the  plate  should  not  be  cut  so  that  these  edges  are 
shorter  than  the  opposite  edges. 

3.  When  a  double  system  of  diagonals  is  used,  as  shown  in  Fig.  Ill, 


the  two  single-angle  members  on  opposite  sides  of  any  plate  may  be 
made  to  overlap  in  order  to  take  one  rivet  in  common.  The  adjacent 
rivets  must  be  spaced  far  enough  from  the  edges  of  the  angles  to  allow 
sufficient  driving  clearance  (page  73  :  5).  The  angles  of  such  double 
latticed  girders  should  be  riveted  at  their  intersections,  with  or  without 
washers. 

4.  All  members  which  are  composed  of  two  angles  should  be  fastened 
together  by  means  of  stitch  rivets,  spaced  as  explained  on  page  69  :  4. 
The  spacing  in  a  tension  web  member  may  be  made  the  same  as  that  in 
a  similar  compression  member  if  by  so  doing  the  members  are  made 
alike. 

5.  Typical  connections  for  roof  trusses  are  shown  at  the  centers  of 
both   LG  1  and   LG  2,  Figs.   110  and   111.     A  girt    connection  is  also 
shown  at  the  center  of  LG  1. 

6.  A  latticed  girder  is  often  used  as  a  "  stiffening  girder."     It  is 
placed   alongside  a  long-span  crane  girder  with  either  the  top  or  the 
bottom  chord  at  the  proper  elevation  so  that  it  can  be  connected  to  the 
top  chord  of  the  crane  girder  by  means  of  tie  plates  and  lattice  bars; 
in  this  way  the  crane  girder  is  stayed  against  buckling  under  the  effects 
of  transverse  thrusts  of  the  crane  due  to  swinging  loads,  etc.     Thus 
LG  1  is  provided  with  holes  in  the  bottom  chord  to  correspond  to  those 
in  the  top  flange  of  G  2,  Fig.  103.     In  this  case  the  stiffening  girder  is 
to  be  placed  between  two  crane  girders,  and  hence  has  holes  in  both 
sides. 


CHAPTER  XX 
ROOF   TRUSSES 

SYNOPSIS:  Directions  are  given  for  making  drawings  of  typical  trusses  which  support 
ordinary  pitched  roofs.  "Flat  roofs"  are  usually  supported  either  by  beams,  or  by 
trusses  similar  to  latticed  girders. 


1.  Steel  roof  trusses  are  used  in  mill  building  construction,  or  where- 
ever  a  comparatively  large  area  is  to  be  covered  without  the  use  of 
intermediate  supports.  The  comparatively  flat  roofs  in  office-building 
construction  are  usually  supported  by  beams  (page  90  :  1).  "Flat 
roofs  "  which  are  pitched  just  enough  to  provide  proper  drainage  are 


simplest  form  it  has  only  a  single  strut  at  the  center  of  each  top  chord, 
but  for  longer  spans  additional  panels  are  added,  as  shown  at  a  and  at  b. 
In  the  Fink  truss  the  top  chord  is  divided  into  an  even  number  of  equal 
panels,  and  the  struts  are  at  right  angles  to  the  top  chord;  the  number 
of  panels  may  be  doubled  by  the  insertion  of  another  strut  in  the  center 


a.  FINK 


b.FlUK  (.CAMBERED) 


C,  FAN  (ODD  PANELS)  d.  FAN  (EVEN  PANELS) 


e.  BALTIMORE 


&  HOWE 


g.  PRATT 


h.  FLAT  WARREN  J.   SAW  TOOTH 

Fig.  113.   Types  of  Roof  Trusses. 


Glass  of  Lomres 


k,  SAW  TOOTH 


.  FINK  WITH  MONITOR  AND  LEANTOS 


carried  over  long  spans  by  "flat  "  trusses  (Fig.  113  (h)),  which  resemble 
latticed  girders  except  that  the  top  chords  are  inclined  slightly. 

2.  The  more  common  types  of  roof  trusses  are  shown  in  Fig.  113. 
Compression  members  are  indicated  by  heavy  lines,  and  tension  mem- 
bers by  fine  lines ;  dotted  lines  represent  members  which  receive  no 
stress  from  the  usual  loads  but  which  are  generally  added  to  support 
intermediate  loads,  to  prevent  a  member  from  sagging,  or  to  give  greater 
rigidity  to  a  structure.  The  "Fink  "  truss,  or  a  modification  of  it 
called  the  "Fan  "  truss,  is  well  adapted  to  most  requirements.  In  its 


113 


of  each  panel.  If  it  is  desired  to  increase  the  number  of  panels  without 
doubling  the  number,  one  or  more  of  the  struts  may  be  replaced  by  two 
members  not  at  right  angles  to  the  top  chord,  and  the  truss  becomes  a 
"Fan  "  truss  as  shown  at  c  and  at  d.  The  "Baltimore  "  truss,  e,  and 
the  "Howe  "  truss,/,  are  used  more  for  wood  construction.  The  normal 
struts  in  the  Baltimore  truss  divide  the  top  chord  into  equal  panels; 
since  two  of  these  struts  meet  at  the  center,  the  pitch  of  the  truss  cannot 
be  assumed  but  it  must  be  calculated  to  correspond  to  the  length  of  the 
span  and  to  the  number  of  panels.  Vertical  members  divide  the  "  Howe  " 


114 


PART   II  —  STRUCTURAL  DRAFTING 


truss,  /,  and  the  "Pratt  "  truss,  g,  into  equal  panels.  The  diagonals  of 
a  Howe  truss  are  in  compression,  while  those  of  a  Pratt  truss  are  in 
tension  as  in  bridge  trusses,  (page  120  :  2) ;  note  that  in  either  case  the 
diagonals  in  the  roof  trusses  and  in  the  corresponding  parallel  chord  trusses 
slope  in  opposite  directions.  Trusses  may  be  cambered  as  shown  at  b, 
to  increase  the  under  clearance  in  the  center  of  the  building  without  a 
corresponding  increase  in  the  height  of  the  walls;  the  horizontal  chord 
is  used  much  more  commonly.  "Saw-tooth  "  roofs  are  used  to  provide 
a  more  satisfactory  lighting  system  within  the  buildings;  the  vertical, 
or  nearly  vertical  portions  of  the  roof  are  so  placed  that  the  northern 
light  (in  the  northern  hemisphere)  can  pass  through  the  glazed  surfaces, 


to  avoid  flexure  in  the  top  chords;  the  designer  must  anticipate  the 
spacing  with  sufficient  accuracy  so  that  he  can  determine  the  proper 
number  of  panels  and  ascertain  whether  the  top  chord  must  be  designed 
for  combined  compression  and  bending.  The  exact  spacing  of  the 
purlins  is  left  for  the  draftsman;  it  necessarily  depends  upon  the  style 
of  the  roofing.  If  tiles  rest  directly  upon  the  purlins  the  spacing  must 
conform  to  the  lengths  of  the  tiles.  For  any  form  of  roofing  which  is 
supported  by  wooden  sheathing,  the  purlins  should  be  so  placed  that 
commercial  lengths  of  lumber  may  be  used  without  excessive  waste. 
Commercial  lengths  of  lumber  are  usually  multiples  of  2  feet.  The  roofing 
which  is  most  used  for  mill  buildings  is  corrugated  steel,  and  when  this 


Fig.  114.  Types  of  Heel  Connections. 


the  direct  sunlight  being  excluded.  Ventilation  or  light  is  often  ob- 
tained by  raising  the  central  portion  of  the  roof  by  means  of  a  "monitor  " 
or  "clearstory  "  as  shown  at  m. 

1.  The  "  pitch  "  of  a  symmetrical  roof  truss  is  the  ratio  of  the  rise 
to  the  span.     The  slope  of  the  roof  or  tangent  of  the  angle  between  the 
top  and  the  bottom  chords  is  not  equal  to  the  pitch,  but  to  twice  the 
pitch.     Thus  the  slope  of  a  j  pitch  roof  is  6  in  12.     \  pitch  trusses  are 
used  most  extensively,  other  common  pitches  being  £,  J,  and  30°. 

2.  Purlin  Spacing.  —  The  form  of  the  truss  and  the  approximate 
spacing  of  the  purlins  are  generally  determined  in  the  designing  depart- 
ment so  that  the  purlins  and  the  trusses  can  be  properly  designed.     The 
purlins  are  the  longitudinal  members  which  support  the  roof.     If  pos- 
sible, the  purlins  should  be  placed  near  the  panel  points  of  the  trusses 


rests  directly  upon  the  purlins  the  latter  must  be  placed  at  such  intervals 
that  sheets  of  standard  lengths  may  be  used.  Corrugated  steel  sheets 
vary  in  length  by  multiples  of  6  inches  from  48  to  126  inches.  As  far 
as  possible  the  sheets  extend  over  two  purlin  spaces.* 

3.  Roof  trusses  may  rest  directly  upon  masonry  walls  or  they  may  be 
supported  by  girders  or  trusses,  but  more  frequently  they  are  riveted  to 
columns.  The  type  of  heel  connection  depends  not  only  upon  the 
form  of  support  but  also  upon  the  detail  of  the  cornice  at  the  eaves; 
this  in  turn  is  dependent  upon  the  style  of  the  roof  covering  and  of  the 

*  For  a  fuller  treatment  of  different  roofing  materials  and  for  more  detailed  informa- 
tion regarding  corrugated  steel  see  Ketchum's  "Steel  Mill  Buildings"  or  "Structural 
Engineers'  Handbook,"  or  Tyrrell's  "Mill  Buildings,"  McGraw-Hill  Book  Co.,  Inc., 
New  York. 


CHAPTER  XX 


ROOF  TRUSSES 


115 


side  walls.  Some  of  the  more  usual  forms  of  heel  plates  are  illustrated 
in  Fig.  114;  the  different  features  shown  often  occur  in  other  com- 
binations. 

1.  Arrangement  on  Sheet.  —  The  members  of  a  roof  truss  are  drawn 
in  the  same  relative  position  which  they  occupy  in  the  completed  struc- 
ture.    This  is  usually  done  even  though  the  truss  is  shipped  "knocked 
down,"  i.e.,  each  chord  and  web  member  shipped  separately.     If  a  truss 
is  symmetrical  about  the  center,  or  nearly  so,  only  one-half  need  be 
shown  on  the  drawing.     A  typical  drawing  for  a  roof  truss  is  shown  in 
Fig.  116. 

2.  A  system  of  working  lines  is  first  laid  down  upon  the  drawing, 
and  all  dimensions  are  referred  to  these  lines.     These  lines  represent 
approximately  the  lines  of  stress  of  the  different  members,  and  at  each 
apex  the  lines  should  meet  in  a  common  point  (compare  page  108  :  5). 
The  rivet  lines  of  angles  are  almost  always  used  as  working  lines  in- 
stead of  lines  through  the  centers  of  gravity;   when  two  rivet  lines  are 
used  in  one  leg,  the  one  nearer  the  back  of  the  angle  is  chosen.     The 
working  lines  may  be  laid  down  to  scale  as  soon  as  the  effective  length 
and  the  rise  (or  the  pitch)  are  known.     The  panels  may  be  made  equal 
by  means  of  any  convenient  scale,  and  all  working  lines  may  be  drawn 
even  if  the  lengths  are  unknown.     The  effective  length  of  span  is  the 
distance  between  the  centers  of  the  columns  or  the  centers  of  the  bear- 
ings.    A  scale  of  f"  =  1'  (or  1"  =  1'),  is  desirable  for  the  details,  but 
if  a  truss  is  too  large  to  permit  the  use  of  the  same  scale  for  the  working 
lines,  they  may  be  plotted  to  a  smaller  scale  (a  decimal  scale  if  desired). 
As  soon  as  the  working  lines  are  plotted  the  corresponding  dimension 
lines  should  be  drawn;  these  lines  should  be  so  placed  that  they  will  not 
interfere  with  each  other  or  with  the  details  which  are  to  be  added 
later.     Usually  an  experienced  draftsman  can  anticipate  the  final  posi- 
tion of  these  lines;   the  beginner  should  use  other  drawings  as  a  guide, 
and  arrange  the  lines  to  the  best  of  his  ability  even  though  some  of  them 
may  have  to  be  changed  later.     It  is  important  to  have  dimension  lines 
upon  which  to  record  the  computed  dimensions  between  the  working 
points;   these  dimensions  should  then  be  determined  and  recorded  upon 
the  lines.     The  computation  may  be  simplified  by  the  comparison  of 
similar  triangles;   thus  for  example,  if  the  half -span  and  the  rise  of  the 


Fink  truss  shown  in  Fig.  115  are  known,  all  but  two  lengths  may  be 
found  by  proportion. 

In  this  truss  the  total  slope  distance  or  hypotenuse  C  should  be  found  from  A  and  B 
by  means  of  a  table  of  squares  (or  from  A  and  the  pitch  by  logarithms).  This  distance 
should  be  divided  into  four  equal  parts;  if  not  equally  divisible,  some  of  the  panels 
may  be  made  ^j"  longer  than  the  others  in  order  to  avoid  thirty-seconds  and  yet  main- 
tain the  proper  total.  The  strut  of  length  D  bisects  the  top  chord  and  forms 
two  equal  right  triangles,  one  vertex  being  at  the  heel  and  the  other  at  the  peak. 
Each  of  these  triangles  is  similar  to 
the  original  half-truss  for  the  angles 

are  equal;    therefore  the   length  D 

ft 
bears  the  same  relation  to  its  base  — 

£ 

that  the  rise  B  bears  to  the  half-span 

fj 
A.    From  D  and   ^  the  hypotenuse 

E  may  be  obtained  by  squares  or  by 
logarithms.  The  remaining  distances 
may  be  found  as  indicated  on  the 
figure. 

It   is   better  to   compute   the 

sides  of  the  larger  triangles  and 

to  get  the  sides  of  the  other  similar  triangles  by  division,  rather  than 

to  compute  the  shorter  lengths  and  obtain  the  others  by  multiplication. 

In  this  way  the  computed  lengths  may  be  taken  to  the  nearest  fV", 

and  the  corresponding  shorter  lengths  will  necessarily  result  within  TV 

of  the  true  values. 

3.  Form  of  Members.  —  The  top  chord  of  a  roof  truss  is  usually 
composed  of  two  angles  with  the  outstanding  legs  along  the  upper  edge. 
In  order  to  stiffen  the  truss  laterally  the  longer  legs  are  often  outstanding, 
the  shorter  legs  being  vertical.  When  the  purlins  cannot  be  placed  at 
panel  points  of  the  truss,  the  top  chord  must  be  designed  to  resist  bend- 
ing as  well  as  direct  compression;  in  this  case  either  the  longer  legs  are 
placed  vertically  or  else  a  web  plate  is  inserted  to  form  a  T-shaped 
member,  as  shown  in  Fig.  114  (c).  The  bottom  chord  is  usually  com- 
posed of  two  angles  with  the  longer  legs  vertical,  the  outstanding  legs 
being  along  the  lower  edge.  Two  channels  are  sometimes  used  if  the 
bottom  chord  is  designed  to  support  a  small  hoist  or  other  direct  load. 


116 


PART   II  —  STRUCTURAL   DRAFTING 


&    Jff.?6xi*3i6*fly    for  AH  113 

// Open  holes  in  angles  rorXH1,2,3 


f-SOShop  rivers  in  AH3.  XH3 


REQUIRED 

1 

HALF  TRUSS 

AH2" 

I 

tt           t  • 

AH  21- 

/ 

rl                       tl 

AH3 

1 

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AH4 

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„                       „ 

XH2L 

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XH3 

6 

J30TT.  CHORDS 

\HHI  \ 

4 

HANGERS 

FL2 

RIVETS 

HOLES js"l/mCSS  HOTtD\ 
WASHEKS  2$ 


SHEETS  3  AND  4  SHOULD 
BE  WORKED    TOGETHER, 

I  SEE    OPPOSITE    PAGE) 

ROOF  TRUSSES 
FUflNACE  BUILDING 
METROPOLITAN  STffL  CO. 

BOSTON,    MASS. 

UNIVERSITY  BRIDGE  COMPANY 

WORCESTER 

IARGEOF        M.G..O. 


MAOE   BV 
CH'K'D 


H.  T.B.  e/,5/fa 


1776 


Fig.  116.   Typical  Drawing  for  a  Roof  Truss. 


CHAPTER  XX 


ROOF  TRUSSES 


117 


REQUIRED 

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HALF   T/ti/SS 

AH  I" 

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AHI  <• 

1 

*                            » 

XH/K 

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2 

HANGERS 

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MEI 

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ME  2 

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2 

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MNI" 

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„ 

MN2 

£ 

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MN3 

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MFI 

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MF/n 

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SHF.C  TS  3  AND  4  SHOULD 
BE  WORKC.D  TOGETHER 

fSCC  OPPOSITE  PA&ll 


ROOF  TRUSSES 

fURNACE  BL//LDIN6 

METROPOLITAN  STEEL  CO. 

BOSTON.  MASS. 

UNIVERSITY  BRIDGE  COMPANY 

WORCESTER  PLANT 
M  G.O. 


HUfsnc*mDw* 

WASHERS 2$* fe    CM.K,DBy  H.T.B.*/W>6 


Fig.  117.   Gable  Girts  and  Monitor  Framing. 


118 


PART  II  —  STRUCTURAL  DRAFTING 


The  web  members  are  composed  of  one  or  two  angles  with  the  longer 
legs  vertical.  The  outstanding  legs  may  be  along  either  edge,  but  for 
the  sake  of  appearance  some  systematic  arrangement  should  be  adopted. 
More  frequently  the  backs  of  the  angle  are  downward  because  the 
members  appear  to  be  stronger  when  viewed  from  below;  as  a  matter 
of  fact  the  compression  members  are  not  so  strong,  although  the  differ- 
ence is  negligible.  It  is  sometimes  desirable  to  turn  one  member  with 
the  back  on  the  opposite  edge  if  by  so  doing  two  members  or  two  con- 
nection plates  may  be  made  alike. 

1.  The  different  members  of  a  truss  are  connected  by  means  of  gusset 
plates.     The  number  of  rivets  required  in  each  member  is  determined 
from  the  stress  in  the  member,  as  explained  on  page  233  :  2.     The  shape 
and  the  dimensions  of  the  gusset  plates  are  determined  graphically  by 
means  of  layouts,  as  explained  on  page  76  :  1.     When  a  continuous  web 
plate  is  used  between  the  angles  of  the  top  chord  a  web  member  may  be 
connected  directly  to  this  plate  without  the  use  of  gusset  plates,  pro- 
vided there  is  room  for  the  proper  number  of  rivets;   otherwise,  part  of 
the  web  plate  must  be  replaced  by  a  gusset  plate,  suitable  splices  being 
used  to  connect  them.     The  size  of  a  gusset  plate  may  sometimes  be 
reduced  if  the  outstanding  leg  of  an  angle  is  connected  to  the  plate  by 
means  of  a  "lug  "  or  connection  angle  as  shown  in  Fig.  118  (a).     One  leg 
only  is  connected  as  a  rule  unless  the  number  of  rivets  exceeds  7  or  8. 

2.  Each  truss  member  which  is  composed  of  two  angles  should  have 
the  angles  fastened  together  by  stitch  rivets,  as  explained  on  page  69  :  4. 
Members  composed  of  two  channels  are  fastened  similarly  by  pairs  of 
rivets  with  a  1\"  or  3"  bar  between,  instead  of  a  washer,  as  shown  in 
Fig.  118  (a).     A  careless  mistake  quite  common  among  draftsmen  and 
tracers  is  to  show  stitch  rivets  in  members  composed  of  single  angles. 
This  is  not  a  serious  blunder,  but  unless  it  is  detected  in  the  templet  shop 
it  may  cause  the  punching  of  extra  holes. 

3.  Center  Hanger.  —  A  light  auxiliary  member  or  "hanger  "  is  often 
used  as  an  intermediate  support  for  the  longer  bottom-chord  members 
even  though  no  corresponding  stress  results  from  the  usual  loads.     Such 
members  are  shown  by  dotted  lines  in  many  of  the  trusses  shown  in  Fig. 
113.     The  purpose  of  these  members  is  twofold.     During  erection  a 
truss  is  assembled  on  the  ground  and  then  raised  into  its  final  position 
as  a  whole,  without  falsework,  by  a  locomotive  crane  or  a  gin  pole;  during 


Fig.  118  (a). 


this  stage  the  bottom  chord  is  in  compression  and  it  may  buckle  unless 

the  long  center  chord  member  is  stayed.     After  the  building  is  completed 

workmen  are  likely  to  attach  block  and  tackle  to  the  bottom  chord  for 

the  purpose  of  lifting  heavy  loads,  even 

though  the  truss  is  not  designed  for  this 

purpose;  this  is  less  serious  if  the  long 

center  panel  is  subdivided.     A   single 

light  angle  is  used  as  a  center  hanger,     ^ 

with  the  rivet  line  at  the  center  of  the    J. 

truss  unless  it  is  offset  to  provide  a 

connection  fora  ridge  strut  (see  below). 

In  either  case  the  connection  at  the  bottom  should  be  made  so  that  the 

bottom  chord  member  is  symmetrical  about  the  center  line  to  simplify 

erection. 

4.  Shipment.  —  A  roof  truss  is  usually  riveted  in  the  shop  completely, 
or  else  in  as  large  sections  as  can  be  shipped;  for  export  each  member  is 
usually  shipped  separately.     The  maximum  height  which  can  be  shipped 
by  rail  is  about  10' -6".     If  the  center  height  exceeds  this  amount  the 
truss  is  shipped  in  sections,  as  shown  in  the  diagram  in  Fig.  116.     Each 
half -truss  is  shipped  on  the  top  chord  as  a  base;  if  the  maximum  normal 
distance  exceeds  10'-6",  smaller  sections  must  be  made.     For  the  meth 
of  marking,  see  page  82  :  2. 

5.  A  ridge  strut  must  be  provided  as  the  compression  member  of  the 
top-chord  bracing  system,  unless  purlins  at  the  peak  serve  the  same  pur- 


Fig.  118  (6).    Details  at  the  Peak. 

pose.  In  a  and  b,  Fig.  118  (6),  are  shown  two  forms  of  purlins  which  alsc 
act  as  struts.  When  the  central  portion  of  the  roof  is  raised  to  the  top  ol 
a  monitor  (Fig.  113  (m))  there  are  no  purlins  at  the  peak  of  the  main  roo: 
and  a  ridge  strut  must  be  provided.  An  I-beam  may  be  used  (c,  Fig 


CHAPTER  XX 


ROOF  TRUSSES 


119 


118  (6)),  but  more  frequently  a  two-angle  member  similar  to  S  5  inverted 
(Fig.  147)  is  employed.  A  continuous  line  of  ridge  struts  is  used  for 
the  full  length  of  a  monitor;  when  two  angles  are  used  in  the  braced  bays 
either  one  or  two  angles  are  used  in  the  intermediate  unbraced  bays.  The 
connection  plate  which  projects  from  between  the  angles  of  the  ridge 
strut  is  inserted  between  two  connection  angles  on  the  peak  plate  of  the 
truss.  The  center  hanger  may  serve  as  a  connection  angle  on  one  side 
of  the  truss,  as  shown  in  Fig.  116;  when  so  used  it  is  offset  so  that  the 
strut  is  in  the  center  of  the  truss'. 

1.  Purlins  are  connected  to  the  top  chord  of  a  truss  by  means  of  con- 
nection angles  as  shown  on  page  315;  the  larger  purlins  have  a  flange 
connection  as  well.     Angles,  channels,  and  Z-bars  are  stronger  if  the 
upper  flanges  or  legs  are  turned  up  the  slope.     Channels  are  usually 
reversed  when  wooden  spiking  pieces  are  used.     Purlins  are  usually 
bolted  in  place,  and  accordingly  the  connection  angles  are  bolted  to  the 
truss,  as  noted  in  Fig.  116.     Purlins  which  act  as  struts  are  connected  by 
more  bolts  than  the  others;  the  strut  connection  is  used  not  only  in  the 
braced  bays  but  for  the  full  length  of  the  building.     In  Fig.  116  the 
purlin  at  panel  point  D  is  a  strut  purlin;   as  shown  in  the  plan,  cross 
bracing  is  used  between  this  purlin  and  the  ridge  strut,  and  also  between 
this  purlin  and  the  eave  strut.     For  convenience,  the  distance  between 
rivet  lines  in  the  top  chord  is  made  a  multiple  of  \"  even  though  special 
gages  are  used  in  the  angles;  a  single  rivet  line  is  used  in  each  angle. 

2.  Bracing  rods  may  be  attached  to  the  top  chords  by  angle  clips,  as 
shown  in  Fig.  116;  these  angles  should  be  so  placed  that  the  rods  will  pass 
through  one  leg  at  right  angles  in  order  that  the  nuts  will  bear  properly. 
Rods  of  minor  importance  may  be  bent  to  pass  through  holes  in  the 
gusset  plates;  holes  are  shown  in  plate  pb  (Fig.  117)  and  in  pj  (Fig.  116) 
for  the  rods  in  the  sides  of  the  monitor.     Similarly,  extra  holes  are 
punched  in  the  top  chord  angles  of  the  monitor  for  rods.     Straight  rods 
may  pass  through  slotted  holes  in  the  gusset  plates  provided  beveled 
washers  (shown  on  page  316)  are  used  to  give  proper  bearing  for  the 
nuts.      Clevises  (page  316)  are  not  used  as  extensively  as  formerly,  be- 
cause other  types  of  connection  are  more  economical. 

3.  Holes  must  be  provided  for  the  bottom-chord  bracing,  as  shown  in 
Fig.  140.     The  plates  are  connected  to  the  under  side  of  the  angles;  when 
a  connection  angle  is  used  at  the  heel,  the  plate  is  placed  either  between 


the  connection  angle  and  the  bottom-chord  angle  or  else  on  top  of  the 
latter.  The  bracing  plate  which  connects  to  the  truss  at  panel  point  H 
serves  also  as  a  splice  plate  for  the  bottom  chord,  and  the  number  of 
rivets  in  the  vertical  legs  may  be  reduced  accordingly;  a  suitable  plate 
must  thus  be  provided  for  each  truss  even  though  there  are  no  diagonals 
to  be  connected  at  this  point. 

4.  So  many  buildings  are  extended  after  they  have  been  completed, 
even  though  such  extension  was  not  anticipated  at  the  time  of  construc- 
tion, that  it  is  advisable  to  make  certain  provisions  for  future  extension 
whether  specified  or  not.     During  the  author's  experience  one  building 
in  which  no  provision  was  made  for  extension,  was  extended  three  times 
before  it  was  completed  once.     If  the  roof  truss  at  the  end  of  a  building 
is  made  like  an  intermediate  truss  it  does  not  have  to  be  moved  when 
the  building  is  extended.     If  a  special  end  frame  is  made  with  rafters 
supported  by  columns,  not  only  the  frame  but  at  least  one  panel  of  roof 
and  side  covering  must  be  removed.     If  future  extension  is  expected, 
holes  should  be  provided  to  facilitate  such  extension.     It  is  often  as  cheap 
to  punch  a  few  extra  holes  in  one  member  in  order  to  make  it  like  another, 
as  to  save  the  extra  holes  by  means  of  special  notes  which  complicate  both 
the  drafting  and  the  shop  work. 

5.  If  the  ends  of  a  building  are  -to  be  covered  with  corrugated  steel, 
girts  must  be  placed  on  the  gable  end  to  support  it.     When  an  end  truss 
is  used,  the  gable  columns  extend  only  up  to  the  bottom  chord  and  the 
gable  girts  myst  be  attached  to  the  truss.     These  girts-  are  shown  in 
position,  and  on  simple  drawings  they  may  be  added  to  the  drawing  of 
the  truss,  as  in  the  monitor,  Fig.  117.     In  case  the  drawing  would  be  too 
complex  if  this  method  were  adopted,  a  second  drawing  may  be  used  in 
conjunction  with  the  first.     Thus  in  Fig.  117  the  working  lines  of  Fig. 
116  are  reproduced  and  the  girts  are  superimposed  in  the  proper  position. 
The  truss  members  to  which  girt  connections  are  to  be  added  are  shown 
in  outline,  and  the  new  connections  are  detailed.     The  two  drawings  are 
worked  together  and  a  note  to  that  effect  should  be  added  to  each  draw- 
ing.    The  required  list  on  the  second  sheet  should  contain  those  members 
which  are  made  wholly  or  in  part  from  that  drawing,  while  the  list  on 
the  first  sheet  should  contain  the  members  which  are  made  entirely  from 
that  drawing. 

6.  Small  holes  for  louvres  are  provided  in  the  sides  of  the  monitor. 


CHAPTER  XXI 


BRIDGE   TRUSSES 

SYNOPSIS:  Types  of  trusses  are  shown  and  practical  suggestions  are  given  for  making 
drawings  of  "bridge  trusses. 

1.   When  Used.  —  Trusses  are  used  in  bridges  for  which  plate  girders     indicated:   thus  for  example,  the  "counters  "  in  (a)  to  (g)  inclusrv 
are  not  well  adapted  either  on  account  of  the  length  of  the  span  or  be-     stressed  only  when  a  portion  of  the  bridge  is  loaded,  the  "collision 
cause  of  economic  reasons.     The  limiting  length  of  plate  girders  is     struts  "  in  (c)  and  the  posts  in  (k)  are  used  to  give  intermediate  support 


(f)CAMEL  BACK  OK  INCLINED  CHORD  PRATT 
*  *  I 


(m)  THROUGH  SUBDIVIDED  WARREU 


(H)   DECK  SUBDIVIDED  WARREN 


(/)  THROUGH  WARA£U 


(k)  SUBDIVIDED  WARREN 

Fig.  120.   Types  of  Bridge  Trusses. 


approximately  130  feet,  but  truss  bridges  are  often  used  for  spans  of  100 
feet  or  less  as  well  as  for  longer  spans. 

2.  The  most  common  types  of  trusses  for  ordinary  bridges  are  shown 
in  Fig.  120.  Cantilever,  suspension,  swing,  and  lift  bridges  are  outside 
the  scope  of  this  book.  The  compression  members  are  represented  in  the 
figures  by  heavy  lines  and  the  tension  members  by  fine  lines.  Dotted 
lines  represent  members  in  which  no  direct  stresses  result  from  the  loads 


to  long  compression  members,  and  other  members  are  inserted  simply 
stiffen  the  structure  or  to  hold  other  members  in  place.  The  term 
"Warren  "  is  usually  applied  to  trusses  in  which  both  the  main  tension 
and  compression  web  members  are  inclined,  forming  isosceles  triangles 
with  the  chords,  as  in  (i)  or  (j).  The  most  favorable  slope  of  diagonal  is 
45° ;  when  the  panel  lengths  exceed  25  or  30  feet  they  may  be  subdivided, 
as  shown  in  (k),  (m),  or  (n).  The  Warren  truss  is  used  for  comparatively 


120 


CHAPTER  XXI 


BRIDGE  TRUSSES 


121 


short  deck  bridges,  and  for  through  bridges  of  spans  from  100  to  200  or 
250  feet.  A  "deck  "  bridge  is  one  in  which  the  floor  loads  are  applied 
at  the  upper  chords  and  a  "through"  bridge  is  one  in  which  the  floor 
loads  are  applied  at  the  lower-chord  apices,  and  the  trains  pass  "through" 
the  bridge  between  trusses.  The  "Pratt"  truss  with  parallel  chords, 
(a)  or  (6),  is  used  for  spans  from  100  to  175  feet,  but  for  longer  spans  the 
"inclined  chord  Pratt "  or  "camel  back  "  truss  (/)  is  preferred  in  order 
to  keep  the  stresses  in  the  chords  more  nearly  equal.  For  spans  longer 
than  300  or  350  feet  it  is  economical  to  subdivide  the  panels  by  verticals 
which  extend  to  the  middle  points  of  the  diagonals ;  auxiliary  half 
diagonals  are  added  either  below  the  center  (e)  or  above  the  center  (g). 
If  the  chords  are  parallel,  either  type  of  "Sub-Pratt  "  is  termed  a  "Balti- 
more "  truss,  but  if  the  top  chord  is  inclined  the  truss  is  called  a  "Pettit." 
The  "Howe  "  truss  (c)  or  (d)  is  used  for  wooden  trusses,  but  it  is  not  so 
well  adapted  to  steel  bridges  as  the  Pratt  truss  because  the  compression 
members  (the  diagonals)  are  longer  than  the  tension  members.  The 
"Latticed  "  truss  (h)  was  formerly  used  for  covered  wooden  bridges  but 
it  is  not  well  adapted  to  steel  construction;  the  stresses  are  statically 
indeterminate. 

1.  The  joints  of  bridge  trusses  may  be  either  riveted  or  pin-connected. 
Only  one  pin  is  used  at  each  joint;  a  pin  is  virtually  a  large  bolt  designed 
as  a  cylindrical  beam  (page  278  :  2).     Riveted  joints  are  used  for  spans 
up  to  about  200  feet  in  length,  particularly  on  railways,  for  the  sake  of 
economy,  rigidity,  and  durability.     Pins  are  used  at  the  joints  of  longer 
spans  because  the  secondary  stresses  which  result  from  riveted  joints  are 
less  easily  accounted  for.     Often  the  intermediate  joints  of  the  top  chord 
are  riveted,  even  though  pins  are  used  in  the  end  posts  and  all  other 
members. 

2.  Arrangement  on  Sheet.  —  The  smaller  and  lighter  riveted  trusses 
may  be  drawn  with  the  members  in  position  in  order  to  save  the  duplica- 
tion of  details,  even  though  the  members  are  to  be  shipped  separately,  as 
illustrated  in  Fig.  122.     More  than  one  sheet  may  be  required  in  order 
to  show  all  of  the  necessary  members;    these  sheets  should  be  used  to 
supplement  each  other  and  each  should  bear  a  note  similar  to  that  in 
Fig.  122.     Reference  points  or  lines  may  be  used  to  indicate  where  the 
dimensions  of  one  sheet  end  and  those  of  the  next  sheet  begin.     For 


example,  the  connections  at  panel  points  L  2  and  U  2  are  fully  detailed 
in  Fig.  122 ;  on  the  next  sheet  these  panel  points  would  be  repeated  and 
the  working  lines  and  the  principal  dimensions  would  be  made  to  extend 
to  these  points.  Enough  of  the  gusset  plates  and  other  details  should 
be  shown  in  outline  so  that  the  extent  of  each  dimension  can  be  identi- 
fied, but  beyond  this  no  attempt  should  be  made  to  duplicate  details 
which  are  completely  shown  on  the  first  sheet.  If  necessary  a  reference 
line  may  be  drawn  on  each  sheet  similar  to  the  line  X-X,  Fig.  101. 
Each  member  of  the  larger  trusses  is  detailed  separately  to  avoid  crowd- 
ing. All  vertical  members  are  preferably  drawn  vertically  if  the  size  of 
the  sheet  will  permit,  and  all  horizontal  members  are  drawn  horizontally, 
i.e.,  lengthwise  of  the  sheet;  riveted  diagonal  members  are  usually  drawn 
either  vertically  or  horizontally  in  order  to  save  space.  Eye  bars  are 
drawn  on  small  sheets  or  printed  forms  (page  174  :  2).  For  the  sake  of 
uniformity  the  members  of  the  left  half  of  the  truss  on  the  far  side  of  a 
bridge  are  shown  on  the  drawings. 

3.  When  members  are  drawn  in  position  great  care  must  be  taken  to 
adopt  the  best  arrangement  of  views  and  of  dimension  lines  to  avoid 
unnecessary  crowding.  The  position  of  the  main  elevation  view  of  each 
member  is  necessarily  determined  as  soon  as  the  working  lines  are  laid 
down.  The  proper  relation  between  views  must  be  maintained,  but  views 
other  than  the  front  views  may  generally  be  placed  so  that  they  will  not 
interfere  with  any  other  member;  when  this  is  not  practicable  a  view 
should  be  so  placed  that  only  unimportant  portions  of  a  view  need  be 
omitted.  For  example,  the  side  view  of  L  l-U  1  (Fig.  122)  is  so  similar 
to  that  of  L  2-U  2  that  it  is  combined  with  it  by  simply  adding  an  extra 
line  of  dimensions  and  the  necessary  notes.  If  a  separate  view  was 
necessary  it  might  be  drawn  at  the  right  of  the  corresponding  front  view, 
part  of  the  member  L  2-U  1  being  omitted  where  necessary.  A  drawing 
may  be  made  clearer  oftentimes  if  one  or  both  ends  of  a  view  are  offset 
from  the  true  projection,  provided  that  such  offset  is  clearly  indicated 
much  as  the  center  line  through  P  6  (Fig.  143)  is  offset  for  P  7.  Space 
may  be  saved,  when  no  ambiguity  is  likely  to  result,  by  combining  a  top 
view  and  a  bottom  sectional  view,  as  illustrated  in  the  end  post  and  the 
top  chord  in  Fig.  122;  only  one  half  of  each  view  is  shown,  both  views 
being  symmetrical  about  the  longitudinal  center  line. 


122 


PART  II  —  STRUCTURAL  DRAFTING 


REQUIRED 

4 

END  POSTS 

EP 

4 

TOP  CHORDS 

UI-3 

2 

BOTT.  CHORDS 

10-2" 

2 

tf               n 

L02L 

4 

POSTS 

LI-UI 

4 

„ 

L2-U2 

4 

DIAGONALS 

L2-UI 

Boh  to  ship  to  LZ -4 


RIVETS  i 
HOLES  % 


TRUSSES 

DERBY    AVE.  BRIDGE 
OVER  C.R.R.OF N.J. 

NEWARK.  N.J. 

UNIVERSITY  BRIDGE  COMPANY 
™*™'£lktjd-?8j?^-' 13 


Fig.  122.   Pony  Truss  for  Highway  Bridge. 


CHAPTER  XXI 


BRIDGE  TRUSSES 


123 


1.  Shipping  Marks.  —  Members  of  bridge  trusses  are  identified  by 
the  marks  of  the  panel  points  between  which  they  extend,  as  explained 
on  page  82  :  1.     It  is  convenient  to  have  a  small  key  diagram  on  each 
sheet  to  show  the  location  of  each  member  detailed  on  that  sheet,  as 
illustrated  in  Fig.  125  and  128. 

2.  Camber.  —  Bridge  trusses  are  slightly  arched  or  "cambered"  so 
that  they  will  assume  the  desired  form  under  full  load.     The  amount  of 
camber  should  equal  the  maximum  deflection  so  that  the  track  will 
approach  a  straight  line  as  the  load  is  applied.     The  position  of  the  panel 
points  should  be  based  upon  the  amount  of  deflection,  and  the  lengths  of 
members  should  be  determined  accordingly.     For  long  spans  the  deflection 
should  be  worked  out  accurately,*  but  for  spans  up  to  about  300  feet 
approximately  the  same  results  may  be  obtained  by  making  the  lengths 
of  the  top  chord  members  slightly  greater  than  the  lengths  of  the  bot- 
tom chord  members.     Instead  of  both  shortening  the  lower  chord  and 
lengthening  the  upper  chord,  it  is  more  convenient  to  make  the  bottom 
panel  lengths  equal  to   the  quotient  found  by  dividing  the  effective 
span  by  the  number  of  panels,  and  to  increase  the  upper  panel  lengths 
enough  to  provide  for  the  combined  change  of  length  in  both  chords. 
The  amount  of  this  increase  for  horizontal  top  chords  or  for  the  hori- 
zontal components  of  inclined  top  chords  is  ^V  inch  for  every  5  feet. 
The  mean  panel  lengths  are  used  in  finding  the  lengths  of  the  diagonal 
members.     See  next  paragraph. 

3.  In  pin-connected  bridges  it  is  well  to  note  the  size  of  the  pin  holes, 
as  in  Fig.  127,  in  order  to  show  the  size  of  the  pins  as  well  as  the  amount 
of  clearance  allowed  for  driving  the  pins.     This  clearance  is  usually 
aV  (or  jV)  of  an  inch  and  it  should  be  considered  in  determining  the 
lengths  of  the  chords  and  diagonals.     Thus  if  the  computed  length  of  a 
compression  member  falls  about  midway  between  sixteenths  the  next 
larger  sixteenth   should   be   chosen.      The  lengths  of    eye-bar  tension 
members  may  be  dimensioned  to  thirty-seconds,  the  full  clearance  of 
sV  being  deducted  from  the  calculated  length. 

4.  Types  of  Members.  —  The  usual  forms  of  top-chord  or  end-post 
members  are  composed  either  of  two  channels  and  a  cover  plate  as  in 
Fig.  122,  or  of  two  webs,  four  angles,  and  a  cover  plate  as  in  Fig.  124. 

*  See  Kirkham's  "Structural  Engineering,"  McGraw-Hill  Book  Co.  Inc.,  New  York. 


A  cover  plate  is  used  on  the  top  to  furnish  protection  from  the  weather, 
but  batten  plates  and  lattice  bars  are  used  on  the  bottom  to  simplify 
the  connection  of  the  web  members.  A  common  form  of  bottom  chord 
for  light  trusses  is  made  of  four  angles  latticed,  as  in  Fig.  122;  for  heavier 
trusses  four  angles  with  side  plates  are  used,  as  in  Fig.  125.  A  solid 
horizontal  web  plate  is  impractical  because  proper  drainage  cannot  be 
provided;  tie  plates  may  be  used  as  in  Fig.  125,  or  batten  plates  with 
lattice  bars  as  in  Fig.  122.  Riveted  diagonals  and  posts  may  be  made 
of  four  angles,-  with  a  web  or  with  lattice  bars,  as  in  Figs.  126  and  122. 
Vertical  posts  and  hangers  should  have  solid  webs  opposite  the  floor- 
beam  and  top-strut  connections,  even  though  lattice  bars  are  used  for 
the  remaining  portion.  Posts  of  Pratt  trusses  are  often  made  of  two 
channels  latticed.  When  single  latticing  is  used  on  opposite  faces  of  a 
member  the  bars  should  alternate,  as  shown  in  Fig.  129.  Batten  plates 
and  lattice  bars  should  be  so  placed  that  ample  room  is  left  for  driving 
all  field  rivets.  One  or  two  bars  may  have  to  be  shipped  bolted,  as  in 
Fig.  129,  so  they  may  be  removed  temporarily  to  facilitate  driving  the 
rivets.  For  the  design  of  lattice  bars,  see  page  216  :  4;  for  the  spacing 
of  them,  see  page  70  :  1. 

5.  Milling.  —  The  ends  of  chord  members  and  end  posts  are  milled. 
This  is  especially  important  in  trusses  with  riveted  joints  in  order  that 
stresses  can  be  transmitted  by  direct  bearing.     At  pin-connected  joints 
clearance  of  about  f  is  left  between  the  milled  surfaces  to  permit  inde- 
pendent action  of  the  members  about  the  pins.     When  the  members 
are  not  in  the  same  straight  line  a  mitered  joint  is  used,  the  milled 
surfaces  bisecting   the  angle  between   members.     The   slope  of   each 
mitered  joint  should  be  given  to  the  nearest  32nd  of  an  inch  instead  of 
the  usual  16th,  and  also  the  corresponding  angle  should  be  expressed  in 
degrees  and  minutes  to  facilitate  the  setting  of  the  milling  machines  in 
the  proper  position. 

6.  Splices.  —  The  riveted  chords  of  parallel  chord  trusses  are  usu- 
ally spliced  independently  of  the  gusset-plate  connections  of  the  web 
members,  in  order  to  avoid  complications  which  might  arise  if  the  web 
members  and  the  floor  beams  were  connected  at  points  where  the  chords 
change  section.     The  splices  are  placed  as  near  the  gusset  plates  as 
feasible,  and  logically  on  the  sides  of  the  smaller  stresses  (Figs.  124  and 


124 


PART  II  —  STRUCTURAL   DRAFTING 


tSp.  P/.24  k*l:3"{bolt  to  ship) 


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UNIVERSITY  BRIDGE  COMPANY 

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Fie.  124.   Top-chord  Member  for  Riveted  Truss  Shown  on  Next  Page. 


CHAPTER  XXI 


BRIDGE  TRUSSES 


125 


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Fig.  125.   Bottom-chord  Member  for  Riveted  Truss  of  a  Railroad  Bridge. 


126 


PART  II  —  STRUCTURAL  DRAFTING 


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Fig.  126.  Web  Members  for  Riveted  Truss  Shown  on  Preceding  Page. 


CHAPTER  XXI 


BRIDGE  TRUSSES 


127 


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Fig.  127.  End  Post  for  Pin-connected  Truss  Shown  on  Next  Page. 


128 


PART  II  —  STRUCTURAL  DRAFTING 


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Fig.  128.  Top-chord  Member  for  Pin-connected  Truss  of  a  Railroad  Bridge. 


CHAPTER  XXI 


BRIDGE  TRUSSES 


129 


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Note: -Vertical  posts  are  preferab  ly  drawn  vertically  whan  size  of  sheet  permits. 


Rivets  i 
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INTERMEDIATE  POSTS 

200  FT.  S.T.  THRU  PIN.  CONN.  SPAN 

NEW  JERSEY  R.R. 

TRENTON,  N.J. 

UNIVERSITY  BRIDGE  COMPANY 

TrS.°t°H PUNT 

IN  CHABQCOF     C.M.D. 

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Fig.  129.  Posts  for  Pin-connected  Truss  Shown  on  Preceding  Page. 


130 


PART  II  —  STRUCTURAL  DRAFTING 


125).  Inclined  top  chords  must  be  spliced  at  the  panel  points;  this 
usually  necessitates  the  use  of  splice  plates  cut  with  reentrant  angles 
(Fig.  128),  although  these  should  be  avoided  if  possible  on  account  of 
difficult  shop  work  (page  76  :  1,  IX  (4)).  For  determining  the  size  of 
splice  plates  and  the  number  of  rivets  required,  see  page  270  :  2. 

1.  Reinforcing  Plates.  —  Channel  webs  and  the  web  plates  of  built 
members  are  seldom  thick  enough  to  transmit  the  proper  stresses  to 
pins.     The  webs  of  pin-connected  members  may  be  reinforced  by  aux- 
iliary plates  to  furnish  sufficient  bearing  area  on  the  pins.     When  the 
ends  of  two  compression  members  bear  on  opposite  sides  of  a  pin,  extra 
plates  should  be  added,  or  one  of  the  reinforcing  plates  on  each  side  of 
each  member  should  be  extended,  to  surround  the  pin;    these  plates 
should  not  be  riveted  to  the  other  member  (Fig.  127).     To  avoid  inter- 
ference, these  plates  may  be  placed  outside  of  the  webs  on  one  member 
and  inside  on  the  other.     The  purpose  of  these  plates  is  to  hold  the 
members  in  position  during  erection  and  also  to  keep  water  out  of  the 
joints.     For  determining  the  size  of  reinforcing  plates  and  the  number 
of  rivets  required,  see  Chapter  XLII,  page  284. 

2.  It  is  often  necessary  to  use  countersunk  or  flattened  rivets  to  pre- 
vent the  interference  of  different  members  during  erection.     Shopmen 
are  accustomed  to  look  for  such  rivets  in  certain  usual  places  so  it  is 
sufficient  to  show  them  by  the  proper  conventional  sign  (page  40  :  6). 
When  rivets  are  countersunk  or  flattened  in  unusual  places,  or  when  they 
are  so  inconspicuous  on  the  drawing  that  they  are  likely  to  be  over- 
looked, a  note  should  be  added,  as  explained  on  page  40  :  6.     Some  of 
the  more  usual  places  where  the  rivets  must  be  countersunk  or  flat- 
tened are:    (a)  in  the  main  plates  of  the  shoes  which  bear  upon  the 
rollers  or  bed  plates;   (6)  in  chords,  posts,  or  shoes,  to  allow  for  eye-bar 


heads,  for  pin  nuts,  or  for  the  overlapping  reinforcing  plates  mentioned 
in  the  preceding  paragraph  (Fig.  127) ;  (c)  in  reinforcing  plates  or  fillers 
under  splice  plates  (Fig.  128) ;  (d)  in  the  top  of  the  end  post  under  the 
connection  of  the  portal  bracing  in  order  to  reduce  the  number  of  fiek 
rivets  (Fig.  127) ;  (e)  in  posts  where  rivets  are  required  in  addition  to 
the  field  rivets  of  the  floor-beam  connections  (Fig.  129).  Field  rivete 
should  be  so  spaced  that  they  need  not  be  countersunk;  thus  in  Fig 
128,  ample  clearance  is  allowed  for  placing  the  pin  nut  in  position.  Th< 
rivets  which  hold  the  angles  and  the  reinforcing  plates  to  the  web  plates 
are  countersunk  underneath  the  splice  plate  so  they  can  be  driven  ir 
the  shop;  note  the  manner  of  indicating  these  rivets  by  broken  lines  t( 
show  that  they  are  countersunk  back  of  the  plate  instead  of  in  the  plate 

3.  Protection  from  the  Weather.  —  Joints  may  be  partially  protectec 
from  the  weather  by  splice  plates  or  by  reinforcing  plates  as  described  ii 
the  preceding  paragraphs.     Joints  which  are  made  at  the  upper  pane 
points  may  be  protected  on  top  by  making  the  connection  plates  for  th 
top  lateral  bracing  extend  entirely  across  the  chords.     Care  must  b 
taken  not  to  interfere  with  the  free  action  of  a  pin-connected  joint  b; 
riveting  these  plates  to  both  members.     Bottom  chord  members  an< 
joints  should  be  so  arranged  that  no  rain  pockets  are  formed.     Drai: 
holes  should  be  provided  in  the  larger  bracing  plates  to  prevent  th 
accumulation  of  water  (Fig.  125). 

4.  Clearance  should  be  allowed  to  facilitate  the  erection  of  we 
members  between  the  gusset  plates  which  are  attached  to  the  chord; 
The  out  to  out  dimensions  of  the  web  members  should  be  made  5  lei 
than  the  clear  distance  between  the  plates. 

5.  The  method  of  holding  a  "  counter  "  in  the  proper  position  on  tr. 
pin  by  means  of  a  notched  plate  is  illustrated  by  plate  pd,  Fig.  129. 


CHAPTER  XXII 
COLUMNS 

SYNOPSIS:    Specific  suggestions  with  illustrations  are  given  for  making  working 
drawings  of  columns  for  different  types  of  structures. 


1.   Steel  columns  form  the  principal  supports  of  all  steel  structures 

other  than  bridges  and  similar  spans  which  rest  directly  upon  masonry. 

They  may  be  of  many  different  forms  according  to  the  type  of  structure. 

A  few  typical  columns  of  office-building  and  mill-building  construction 
lave  been  selected  for  illustration.  Many  mill  buildings  and  similar 

structures  have  unusual  or  complicated  connections  so  that  it  is  difficult 
,o  proceed  with  the  drawings  of  the  columns  until  after  the  drawings  of 
,he  connecting  members  have  been  carried  far  enough  to  determine  the 

column  connections.  When  possible  it  is  usually  simpler  to  postpone 
he  column  drawings  until  all  connecting  members  have  been  drawn. 

The  available  time  is  seldom  sufficient  to  permit  this  method,  however, 

because  the  columns  are  the  first  members  to  be  erected.  The  drawings 
or  the  columns  must  logically  be  among  the  first  drawings  sent  to  the 

•shop,  and  connections  for  other  members  must  frequently  be  provided 
jefore  the  drawings  of  those  other  members  have  been  made  or  even 
>egun.  It  is  often  necessary  to  make  a  layout  of  the  more  unusual 
•onnections  to  determine  the  necessary  dimensions  to  be  used  on  the 
•olumn  drawings.  These  layouts  may  later  be  used  by  the  draftsmen 
vho  make  the  drawings  of  the  connecting  members.  Many  types  of 
onnection  recur  so  frequently  that  standards  are  prepared  in  the  draft- 
ng  rooms  of  the  larger  structural  companies.  These  standards  simplify 
he  work  of  the  draftsmen  and  in  many  cases  they  simplify  the  work  of 
he  templet  makers.  In  fact,  wooden  templets  for  typical  connections 
my  often  be  preserved  for  future  use  to  save  making  new  ones  for  sub- 
?quent  contracts. 


131 


2.  It  is  desirable  to  draw  all  members  in  the  same  relative  position 
on  the  sheet  which  they  are  to  occupy  in  the  finished  structure.     Thus, 
columns  are  preferably  drawn  with  their  longer  axes  vertical,  as  in  Fig. 
137.     This  is  not  always  feasible  on  account  of  the  multiplicity  of  details, 
for  more  space  is  available  if  they  are  shown  with  their  longer  axes  hori- 
zontal (i.e.,  lengthwise).     When  the  columns  are  drawn  horizontally  it 
is  customary  to  show  the  base  or  bottom  end  of  the  column  at  the  left  as 
in  Figs.  133  and  135.     It  is  unnecessary  to  draw  the  full  length  of  a 
column  to  the  same  scale  as  the  details.     The  most  common  scale  used 
for  the  details  is  f "  =  1'.     The  extreme  length  of  the  column  is  made  to 
suit  the  available  space  on  the  sheet  allowing  for  the  necessary  views  and 
dimension  lines.     The  details  are  then  placed  at  approximately  propor- 
tional distances  apart  regardless  of  scale.     No  breaks  in  the  views  need 
be  shown  unless  the  drawing  can  be  made  clearer  thereby. 

3.  So  many  different  types  of  columns  *  are  used  by  different  designers 
it  is  impossible  to  show  them  all.     Perhaps  the  three  most  common  types 
are  the  plate  and  angle,  the  plate  and  channel,  and  the  Bethlehem  H-sec- 
tion.     The  drawings  for  the  H-section  are  comparatively  simple  since  the 
main  section  is  rolled  complete  and  no  continuous  lines  of  rivets  are 
required  unless  cover  plates  are  used.     The  connections  are  similar  to 
those  of  other  columns  and  it  seems  unnecessary  to  illustrate  them  here.f 

*  See  Ketchum's  "Structural  Engineers'  Handbook,"  McGraw-Hill  Book  Co.  Inc., 
New  York. 

t  For  typical  connections  see  the  "Catalogue  of  Bethlehem  Steel  Shapes,"  Beth- 
lehem Steel  Co.,  South  Bethlehem,  Pa. 


132 


PART   II  —  STRUCTURAL   DRAFTING 


The  plate  and  channel  columns  are  used  for  office-building  construction. 
The  upper  sections  are  often  made  of  channels  with  lattice  bars,  the 
bars  being  replaced  by  cover  plates  in  the  lower  sections.  As  the  loads 
increase,  the  thickness  of  the  plates  and  the  weights  of  the  channels 
are  increased  and  if  necessary  the  width  of  the  plates  and  the  depth  of 
the  channels  as  well.  The  plate  and  angle  column  is  used  most  exten- 
sively for  mill-building  construction;  it  is  also  used  for  office  buildings. 
Very  light  sections  are  made  of  four  angles  latticed,  but  usually  solid  web 
plates  are  used  instead  of  the  lattice  bars.  For  very  heavy  loads  larger 
angles  are  used  with  cover  plates  riveted  to  their  outstanding  legs. 

1.  Typical  plate  and  channel  columns  are  shown  in  Fig.  133.  They 
are  detailed  for  the  conditions  shown  in  the  diagram  of  Fig.  158  and  in 
the  corresponding  column  schedule  of  Fig.  160.  The  views  of  the 
different  faces  are  often  lettered  for  convenience  in  the  identification 
of  the  details.  The  dashed  lines  of  the  channel  flanges  in  Faces  A  and 
C  need  not  be  drawn  full  length  if  the  drawing  is  equally  clear  without. 
Since  considerable  time  is  required  to  draw  so  many  long  dashed  lines 
it  is  well  to  omit  portions  of  them  whenever  feasible.  Column  AB  1 
shows  the  base  angles  which  connect  to  the  cast-iron  bases.  At  the  top, 
splice  plates  and  angles  are  provided  to  connect  to  the  superimposed 
column  section  composed  of  channels  of  the  same  depth  and  cover  plates 
of  the  same  width  The  lower  end  of  the  connecting  column  would  be 
similar  to  the  lower  end  of  Column  EF  27,  differing  only  in  dimensions 
since  the  column  is  of  a  different  size.  The  ends  of  office-building  columns 
are  milled  so  that  the  loads  may  be  transmitted  by  direct  bearing  (page 
31  :  1).  A  more  complex  splice  is  required  where  the  depth  of  the 
channels  and  the  width  of  the  cover  plates  change.  Such  a  splice  is 
shown  on  the  column  schedule  (Fig.  160) ;  it  is  described  more  fully  on 
page  276  4.  Provision  for  a  similar  splice  is  made  at  the  top  of  Column 
EF  27.  The  projecting  corners  at  the  top  of  the  splice  plates  need  not 
be  cut  (Fig.  277)  if  they  are  to  be  concealed  by  the  fireproofing.  For  the 
size  of  the  fillers  and  the  reinforcing  plates  and  the  number  of  the  rivets 
see  page  276  :  4.  The  spacing  of  the  channels  and  the  gages  are  given 
on  pages  300  and  301.  Note  that  for  a  given  depth  of  channel  the 
distance  out  to  out  of  web  faces  and  the  distance  between  rivet  lines  are 
constant,  while  the  distance  back  to  back  of  webs  and  the  gages  vary 


with  the  weight.  This  is  so  arranged  in  order  to  standardize  the  splice 
plates  and  the  beam  connections  and  also  to  reduce  the  number  of 
different  lengths  of  beams. 

2.  The  important  dimension  is  the  finished  length  and  this  is  prefer- 
ably made  conspicuous.     Since  all  elevations  on  the  diagrams  are  referred 
to  the  finished  floor  line  it  is  important  to  show  each  floor  line  on  the 
column  drawings  and  to  give  the  story  heights.     The  beam  details  are 
located  with  reference  to  these  floor  lines  and  the  rivets  which  fasten  the 
cover  plates  to  the  channels  are  then  dimensioned  to  fill  in  the  spaces 
between  the  details.     Close  spacing  of  four  diameters  is  used  at  both 
ends  of  the  column  (page  69  :  1  (d))  and   near  the  beam  connections. 
Six  inch  spacing  is  allowed  as  a  maximum  for  the  remaining  distances. 

3.  Typical   symmetrical   beam   connections   are   shown   on   Column 
EF  27,  and  special  eccentric  beam  connections  on  Column  AB  1.     The 
whole  load  from  each  beam  is  carried  by  the  seat;   the  top  angle  serves 
to  prevent  the  beam  from  overturning  and  to  help  transmit  the  wind 
stresses  in  the  structure.     The  top  angles  are  left  bolted  so  that  they  may 
be  removed  to  facilitate  erection.     They  are  also  placed  \"  higher  than 
the  theoretical  top  of  the  beam  to  provide  for  the  spreading  of  the  flanges 
of  the  beam  while  cooling  on  the  rolls  during  their  manufacture.     Note 
that  after  the  cover  plates  have  been  riveted  to  the  channels  a  box  section 
is  formed,  the  inside  of  which  is  inaccessible.     In  order  to  provide  for 
the  temporary  removal  and  the  restoration  of  the  bolts  in  the  top  angles 
of  the  connections  on  the  channel  webs  the  bolts  must  pass  through  the 
whole  column.     Unless  a  similar  angle  is  required  directly  opposite,  a 
special  note  must  appear  to  assure  the  punching  of  holes  in  both  channel 
webs  for  through  bolts  (face  D,  AB  1).     The  top  angles  on  the  cover 
plate  faces  are  made  sufficiently  long  to  permit  the  use  of  short  bolts 
through  the  channel  flanges.     If  shorter  angles  were  used,  the  necessary 
through  bolts  would  often  interfere  with  those  through  the  channel 
webs.     The  rivets  in  the  channel  webs  and  some  of  those  in  the  cover 
plates  are  inaccessible  after  the  column  is  assembled;    thus,  the  rivets 
in  the  seat  angles,  stiffening  angles,  reinforcing  plates,  and  fillers  under 
splice  plates,  must  be  driven  before  the  cover  plates  and  channels  are 
bolted  together.     Special  gages  are  used  in  the  6"  legs  of  the  seat  angles 
to  conform  to  the  spacing  of  the  rivets  in  the  channel  flanges.     The 


CHAPTER  XXII 


COLUMNS 


133 


25  3"  'Finished  '  Lenath 


/J^7X-<?  /Column  MarkABI 


23i//z"  Finished  Lenath 


'ake/ Column  MarkEF27 


COLUMNS 

TYPICAL  OFFICE BU/LDI/VS 


HOLES  % 


Fig.  133.   Typical  Office-building  Columns. 


134 


PART  II  —  STRUCTURAL  DRAFTING 


bottom  ends  of  stiffening  angles  need  not  always  be  c"ut  back  as  shown. 
If  concealed  by  the  regular  fireproofing  or  by  walls  or  partitions  they  may 
be  cut  square.  The  draftsman  must  be  familiar  with  the  methods  of 
erection  in  order  to  determine  which  rivets,  if  any,  should  be  flattened  or 
countersunk  to  facilitate  the  insertion  of  the  beams  (see  Column  EF  27). 

1.  Sectional  views  are  drawn  for  each  tier  of  beam  connections  in  order 
to  show  the  holes  in  the  outstanding  legs  of  the  angles.     The  section  is 
sometimes  taken  between  the  top  and  bottom  angles,  but  more  often 
above  the  top  angles  as  shown  in  Fig.  133.     In  order  to  draw  attention 
to  the  fact  that  the  holes  should  be  made  in  both  the  seat  and  the  top 
angles,  the  holes  are  often  shown  in  the  other  views  as  well  (page  40  :  6). 

2.  Fig.  135  illustrates  a  typical  mill-building  column  drawn  for  the 
conditions  shown  in  the  plans  and  diagrams  of  Figs.  155  and  156.     The 
lower  part  of  the  column  is  made  wider  than  the  upper  in  order  that  the 
crane  loads  may  be  transmitted  to  the  column  base  more  directly.     The 
width  of  the  lower  section  is  usually  made  so  that  the  outer  face  of  the 
cover  plate  or  channel  comes  directly  under  the  center  of  the  girder. 
Seat  angles  and  stiffeners  are  used  to  provide  a  suitable  girder  seat  as 
shown.     The  girder  is  secured  against  overturning  by  means  of  a  dia- 
phragm.    The  end  stiffeners  of  the  crane  girder  shown  in  Fig.  103  are 
arranged  to  connect  to  a  diaphragm  similar  to  that  shown  in  Fig.  135. 
Holes  are  provided  in  the  channel  web  for  the  girder  knee  brace  shown 
in  Fig.  140. 

3.  Connections.  —  At  the  top  of  the  column  a  connection  is  provided 
for  the  roof  truss  shown  in  Fig.  116.     The  web  plate  of  the  upper  section 
of  the  column  is  connected  to  the  web  plate  of  the  lower  section  by  means 
of  splice  plates  designed  to  develop  the  full  strength  of  the  upper  web 
(page  276  :  2).     The  outer  angles  are  continuous,  and  the  shorter  angles 
of  the  upper  section  extend  downward  far  enough  so  that  they  may  be 
fully  developed  by  rivets  which  connect  them  to  the  lower  web.     Holes 
are  provided  in  the  outstanding  legs  of  the  continuous  angles  for  the  girts 
and  struts  indicated  on  the  erection  diagram  (Fig.  156)  and  detailed  in 
Fig.  147.     It  is  customary  to  punch  these  holes  in  both  sides  of  the  end 
columns  the  same  as  in  the  intermediate  columns,  although  the  side  girts 
do  not  extend  past  the  center  lines.     These  extra  holes  may  not  all  be 
used,  although  as  far  as  possible  the  girts  on  the  ends  of  the  building  are 


arranged  to  connect  to  them.  The  cost  of  punching  a  few  unused  holes 
does  not  greatly  exceed  the  cost  of  omitting  them  because  of  the  time 
required  to  make  and  to  follow  special  notes,  and  furthermore,  the  wrong 
holes  might  be  omitted.  In  case  the  building  is  later  extended  the  extra 
holes  may  be  used.  The  bottom  strut  at  the  end  of  the  building  (S  7 
Fig.  140)  connects  to  the  flange  of  the  channel  of  Column  C  1  instead  of 
to  the  outer  angles  to  make  a  more  rigid  connection  and  to  reduce  the 
lengths  of  the  struts  and  the  diagonal  sway  bracing.  The  sway  bracing 
connects  to  the  top  of  Column  C  1  on  the  inner  face  by  means  of  a 
bracket  (D  13,  Fig.  140). 

4.  A  typical  column  base  as  described  on  page  290  :  1  is  illustrated  in 
Fig.  135.     An  excessive  number  of  countersunk  rivets  in  the  base  plate 
and  the  cap  plate  should  be  avoided.     It  is  usually  impractical  to  swing 
a  long  column  around  so  that  these  few  rivets  can  be  driven  by  machine 
and  consequently  they  must  be  driven  by  hand  riveters.     Since  these 
rivets  do  not  have  a  very  important  function  their  number  should  be 
reduced  to  the  minimum.     Holes  for  anchor  bolts  are  made  -fs"  or  f " 
larger  than  the  diameter  of  the  bolts  to  facilitate  placing  the  columns  in 
position  when  the  bolts  are  set  first,  or  drilling  holes  in  the  masonry  for 
the  bolts  after  the  steel  is  in  position. 

5.  Milling.  —  A  column  which  supports  crane  runway  girders  is  in- 
variably milled  at  the  base  and  at  the  crane  seat  in  order  that  the  crane 
loads  may  be  transmitted  largely  by  direct  bearing.     The  web  plate  is 
not  always  milled  at  the  seat  along  with  the  angles  and  channel  because 
of  practical  difficulties. 

6.  Most  of  the  vertical  dimensions  to  the  bottom  of  the  column 
extend  only  to  the.  upper  face  of  the  base  plate  instead  of  to  the  extreme 
bottom.  In  this  way  the  dimensions  best  serve  the  templet  maker  and 
the  inspectors  who  use  them  before  the  base  plate  is  in  place.  In  some 
companies,  however,  the  dimensions  extend  to  the  extreme  bottoms  of 
the  column  bases.  Draftsmen  must  be  particularly  careful  to  give  due 
consideration  to  those  dimensions  which  may  be  affected  by  the  thickness 
of  the  base  plate.  When  many  different  connections  appear  on  a  single 
face  of  the  column,  as  in  the  outer  face  of  C  1  and  C  2,  "extension  figures  " 
should  be  given  from  each  connection  to  the  base  plate,  in  addition  to  the 
dimensions  from  one  connection  to  the  next.  The  extension  figures  art 


CHAPTER  XXII 


COLUMNS 


135 


IP/./8*l*/-O"pa 
tL6*4«{*l:6"aa 
16'4"i'2- 


COLUMNS 
rURN/ICE  BU/LD//V6 
METROPOLITAN STE£L  CO. 

BOSTON,  MASS 

UNIVERSITY  BRIDGE  COMPANY 


IN  CHARGE  OF  M-6.O..___ 
CH'K'OBV     H.T.B.8/2//I8 


Fig.  135.   Typical  Crane  Column  for  a  Mill  Building. 


136 


PART  II  —  STRUCTURAL  DRAFTING 


convenient  for  the  templet  makers  and  the  inspectors  so  that  they  can 
locate  all  the  connections  with  a  single  setting  of  the  tape.  The  figures 
are  of  convenience  also  to  the  draftsmen  and  checkers  when  referring  to 
a  drawing  to  obtain  differences  in  elevation  between  connections.  When 
making  the  drawing  the  draftsman  should  record  the  extension  figures 
for  each  connection  as  soon  as  that  connection  is  detailed.  The  dimen- 
sion should  extend  preferably  to  the  point  dimensioned  on  the  diagram, 
as  for  example,  the  back  of  a  girt  or  a  strut  angle.  Similar  connections 
may  then  be  detailed  before  other  types  of  connection  are  designed,  and 
later  the  other  types  may  be  inserted  in  the  proper  places.  After  all 
connections  are  located  the  distance  from  one  connection  to  the  next  may 
be  found  simply  by  subtracting  the  corresponding  extension  figures. 
Some  companies  require  a  complete  line  of  dimensions  from  center  to 
center  of  holes,  but  this  seems  unnecessary,  particularly  when  there  are 
comparatively  few  holes  in  each  group.  If  the  groups  are  located  as 
shown  in  Fig.  135  the  dimensions  can  often  be  taken  directly  from  the 
diagram,  and  if  the  shopmen  are  forced  to  use  these  dimensions  instead 
of  calculated  distances  between  adjacent  holes  one  source  of  error  is 
eliminated. 

1.  Standard  gages  in  column  angles  are  not  used  in  all  cases.     In  the 
outstanding  legs  of  the  main  angles  and  of  the  angles  in  the  diaphragm 
and  similar  places  it  is  desirable  to  make  the  distances  from  center  to 
center  of  holes  a  multiple  of  J"  or  preferably  \" .     Thus  the  use  of  six- 
teenths and  eighths  in  the  main  dimensions  of  connecting  members  is 
avoided.     The  gages  in  the  angles  may  result  in  sixteenths  or  eighths, 
but  the  use  of  small  fractions  is  confined  to  relatively  few  dimensions. 
Similarly,  if  girts  or  other  members  connect  to  column  angles  of  different 
sizes,  more  members  may  be  made  alike  if  the  gages  in  the  column  angles 
are  made  the  same.     For  example,  the  gages  in  5  and  6  inch  legs  may  be 
made  equal,  and  those  in  3J  and  4  inch  legs  also.     A  single  rivet  line  is 
usually  used  in  each  leg,  even  if  5  or  6  inches. 

2.  Two  other  types  of  mill-building  columns  are  shown  in  Fig.  137. 
Column  C  3  is  a  column  for  the  gable  end  of  the  mill  building  illustrated 


in  Fig.  156.  The  end  truss  is  made  similar  to  the  intermediate  trusses 
and  is  designed  to  span  the  full  width  of  the  building  without  intermedi- 
ate supports.  The  chief  function  of  the  gable  column  is  to  support  the 
end  framing  (girts,  struts,  etc.)  below  the  bottom  of  the  truss.  The 
upper  end  of  the  column  is  supported  laterally  by  being  connected  to 
the  roof  truss  at  a  point  where  the  truss  is  braced  in  the  plane  of  the 
bottom  chord;  but  in  order  to  avoid  stresses  for  which  the  truss  is  not 
designed,  the  connection  angles  at  the  top  of  the  column  are  provided 
with  vertical  slots  to  permit  the  free  deflection  of  the  truss.  The  base  is 
designed  to  transmit  the  whole  load  through  rivets  so  that  it  is  unneces- 
sary to  mill  the  column.  In  general,  a  column  is  not  milled  unless  the 
load  is  more  than  about  40,000  or  unless  the  column  is  to  support  a  crane 
or  other  moving  load.  Holes  are  provided  in  the  outstanding  legs  of 
the  column  angles  for  girts  and  struts  as  in  the  columns  of  Fig.  135.* 

3.  Columns  C  4  and  C  5  are  light  latticed  columns  with  provision 
for  a  roof  truss  connection  at  the  top.  An  eccentric  beam  connection 
is  inserted  between  the  two  groups  of  lattice  bars.  Connections  for 
light  lean-to  rafters  and  for  girts  are  shown  in  the  outer  faces.  Sep- 
arate views  of  these  faces  are  drawn  for  the  two  columns  in  order  to 
show  the  differences  clearly.  When  lattice  bars  are  placed  between 
the  angles  as  in  this  type  of  column  the  distance  between  angles  is  not 
constant;  the  distance  may  be  determined  by  the  thickness  of  the 
plates  as  pa  or  pb,  by  the  thickness  of  a  single  lattice  bar,  or  by  the 
thickness  of  two  overlapping  bars.  Consequently  either  the  gages  in 
the  angles  or  the  distance  between  holes  must  vary.  Usually  it  is 
desirable  to  maintain  a  constant  distance  between  holes  so  that  like 
members  may  be  connected  at  different  parts  of  the  column.  Rather 
than  to  dimension  each  group  of  holes  separately  it  is  well  to  omit  the 
gages  altogether  and  to  let  the  templet  maker  make  proper  provision 
for  the  variation;  then  the  distance  between  holes  need  be  dimensioned 
only  once  for  each  view.  For  the  size  of  lattice  bars  and  batten  plates 
see  page  216: 2-3.  No  tie  or  batten  plate  is  needed  at  the  top  because  the 
heel  plate  of  the  roof  truss  will  serve  the  purpose  after  it  is  in  position. 


CHAPTER  XXII 


COLUMNS 


137 


BASE 

1  PI.  14xjxl'-l"ca 

2Ls6*Bxlx  llaa 

2  Fills  6  x  j-x  Sfa 


A.  holes  for  I  bolts 


REQUIRED 

2 

Columns 

C3R 

2 

n 

C3L 

8 

" 

w 

2 

" 

CSR 

2 

" 

C6L 

Rivets  -f 

Holes  llunless  noted 


COLUMNS 
TYPICAL  MILL  BUILDING 


Fig.  137.  Typical  Light  Columns  for  a  Mill  Building. 


CHAPTER  XXIII 
BRACING  SYSTEMS 

SYNOPSIS:  A  discussion  of  the  types  of  bracing  used  under  different  conditions,  with 
illustrations. 


1.  Some  system  of  bracing  is  usually  required  to  secure  a  structure 
against  forces  which  tend  to  distort  or  overturn  it.     These  forces  may 
result  from  the  wind,  from  moving  loads,  or,  during  erection,  from  der- 
ricks or  travelers.     Diagonal  bracing  is  the  most  effective  but  it  cannot 
be  used  where  it  would  interfere  with  the  use  of  the  structure,  as  for 
example  across  doorways.     When  it  is  not  feasible  to  place  diagonals 
entirely  across  the  panel  to  be  braced,  special  brackets,  knee  braces,  or 
portal  struts  may  be  employed.     In  some  structures  the  riveted  joints 
may  give  ample  security  so  that  no  special  bracing  is  required.     In 
other  structures  only  temporary  bracing  is  required  during  erection, 
as  for  example  the  bracing  between  steel  columns  which  are  later  to  be 
imbedded  in  solid  masonry  walls. 

2.  Bracing  systems  with  full  diagonals  may  be  considered  as  trusses 
and  so  designed.     The  chord  stresses  of  these  trusses  are  taken  by  the 
members  to  which  the  bracing  connects,  as  for  example  the  columns, 
the  girders,  or  members  of  other  trusses.     The  "posts"  or  transverse 
compression  members  may  be  either  special  struts  or  else  members 
which  are  already  provided,  such  as  floor,  beams,  cross  frames,  or  pur- 
lins.    The  diagonal  stresses  in  any  panel  may  be  resisted  by  a  single 
member  placed  along  either  diagonal  of  the  panel;   if  in  one  position  it 
will  be  in  tension  but  if  in  the  other  position  it  will  be  in  compression. 
Usually  these  diagonal  members  are  designed  for  tension  and  are  placed 
accordingly.     To  provide  for  forces  which  might  cause  a  reversal  of 
stress,  members  may  be  p'aced  along  both  diagonals  to  form  "cross 
bracing;  "   only  the  diagonal  which  is  in  tension  is  considered  to  act  at 


any  one  time.     The  sizes  of  the  members  and  the  number  of  rivets  are 
often  standardized  for  similar  conditions  in  order  to  simplify  the  design. 

3.  Bracing  systems  with  full  diagonals  should  be  statically  complete; 
that  is,  diagonals  should  not  be  used  unless  they  are  supplemented  by 
the  proper  struts.     Special  struts  are  not  always  required;   for  instance 
an  eave  strut  of  a  mill  building  may  serve  as  a  girt,  as  a  purlin,  and 
also  as  the  end  strut  of  the  bracing  in  three  different  planes,  viz:    the 
vertical  sway  bracing  between  columns,  the  horizontal  bracing  between 
the  bottom  chords  of  the  trusses,  and  the  bracing  parallel  to  the  pla 
of  the  roof  between  the  top  chords  of  the  trusses. 

4.  The  lines  of  stress  of  all  members  which  are  connected  by  a  single 
gusset  plate  should  meet  approximately  in  a  common  point  to  minimize 
the  secondary  stresses.     Adherence  to  this  rule  is  seldom  strictly  en- 
forced, however,  because  a  slight  deviation  will  permit  the  use  of  an 
auxiliary  system  of  working  points,  as  explained  on  page  108  :  5.     A 
plate  which  connects  only  a  single  diagonal  to  another  member  should 
be  so  arranged  that  the  line  of  action  (rivet  line)  of  the  diagonal  will 
fall  within  the  group  of  rivets  which  connect  the  plate  to  the  other 
member,  in  order  to  reduce  the  eccentricity.     See  Fig.  140. 

5.  Arrangement.  —  The  drawings  for  cross  bracing  are  usually  so 
made  that  the  diagonals  are  shown  in  the  proper  relation  to  each  other 
and  to  the  members  to  which  they  connect.     The  system  of  working 
lines  can  then  be  easily  checked,  and  the  connections  to  other  members 
may  be  readily  compared  with  the  drawings  of  the  corresponding  mem- 
bers.    The  centers  of  the  end  holes  in  the  diagonals  are  usually  chosen 


138 


CHAPTER  XXIII 


BRACING  SYSTEMS 


139 


as  working  points.  The  system  of  working  lines  may  be  plotted  to  a 
smaller  scale  than  the  details  in  order  to  save  space;  some  of  the  simple 
diagonals  or  struts  may  be  shown  separately  for  the  same  reason.  In 
the  simplest  form  of  cross  bracing  the  diagonals  are  so  turned  that 
they  may  pass  each  other  without  interference,  as  shown  in  the  cross 
frames,  Fig.  142.  More  frequently  the  outstanding  legs  of  the  two 
angles  are  made  to  face  the  same  way  even  though  one  angle  has  to  be 
cut  and  spliced  at  the  intersection.  In  this  position  they  occupy  less 
space  and  they  are  less  liable  to  interfere  with  other  members;  it  is 
often  necessary  to  turn  them  this  way  to  obtain  the  desired  clear  open- 
ing without  increasing  the  height  or  width  of  a  structure. 

1.  Initial  Tension.  —  Diagonal  bracing  must  be  tight  in  order  to  be 
most  effective.     A  long  diagonal  will  sag  under  its  own  weight  during 
erection  unless  it  is  drawn  tight  before  it  is  bolted  or  riveted.     Con- 
siderable racking  of  the  structure  could  take  place  without  removing 
this  sag  or  stressing  the  member.     In  order  to  make  a  structure  more 
rigid  by  causing  the  diagonals  to  act  at  once,  the  length  from  center  to 
center  of  the  end  holes  is  made  less  than  the  calculated  distance.     The 
member  may  then  be  drawn  into  position  for  bolting  or  riveting  by 
driving  a  tapered  drift  pin  into  the  holes.     Since  the  holes  are  punched 
-iV"  larger  than  bolts  or  rivets  the  member  should  be  shortened  TV"  to 
take  up  the  "play  "  in  the  holes  and  at  least  another  Ty  to  overcome 
inaccuracies  in  punching  and  other  factors.     Tightness  is  thus  insured 
even  though  a  certain  amount  of  initial  tension  may  result.     The  total 
amount  to  be  deducted  from  the  calculated  distance  from  center  to 
center  of  end  holes  should  be  either  \"  or  -fa" ' ,  whichever  will  make  the 
main  dimension  a  multiple  of  5".     In  this  way  the  half  lengths  will  be 
expressed  in  multiples  of  TV",  and  32nds  will  be  avoided.     Sometimes 
the  amount  deducted  is  noted,  as  in  T  1,  Fig.  143.     The  chief  benefit  of 
such  a  note  is  to  give  assurance  that  provision  has  been  made  for  some 
deduction.     No  deduction  should  be  made  for  comparatively  short  stiff 
members  such  as  the  diagonals  in  the  cross  frames  or  the  lateral  bracing 
between  the  girders  of  a  deck  railroad  bridge,  because  it  would  be  diffi- 
cult to  connect  them. 

2.  Connections.  —  The  diagonals  and  the  connection  plates  are  usu- 
ally shipped  separately  although  some  of  the  smaller  plates  may  be 


fastened  to  the  angles.  The  bracing  for  all  bridges  and  many  buildings  are 
fully  riveted  in  the  field.  The  bracing  for  parts  of  some  buildings  may  be 
bolted  if  the  specifications  will  permit.  When  the  field  connections  are 
to  be  bolted,  similar  shop  connections  may  be  bolted  also  (Fig.  140) ;  if 
there  are  other  shop  rivets  to  be  driven  in  the  same  member  it  is  about 
as  cheap  to  use  rivets  instead  of  shop  bolts  in  the  end  connections. 

3..  Special  gages  are  often  used  in  bracing  angles.  The  rivet  line  of 
a  single  angle  is  used  as  the  working  line.  If  this  working  line  is. placed 
in  the  center  of  the  leg  the  connections  may  be  detailed  to  better  ad- 
vantage. The  clearances  on  opposite  sides  are  thus  made  more  nearly 
equal  regardless  of  which  way  the  angle  is  turned  when  erected.  In 
angles  with  legs  less  than  3"  standard  gages  should  be  used  to  allow 
greater  driving  clearance  for  the  rivets  or  bolts. 

4.  Typical  illustrations  have  been  selected  to  show  the  common  forms 
of  bracing  used  in  different  structures.     The  general  arrangements  are 
shown  in  the  erection  diagrams  of  Chapter  XXV  (page  151),  but  the 
details  are  shown  in  the  drawings  of  this  chapter. 

5.  A  mill  building  can  have  no  system  of  bracing  which  obstructs  the 
interior  and  prevents  the  free  movement  of  cranes  or  other  objects. 
Cross  bracing  is  commonly  used  in  the  sides,  the  ends,  and  the  roof, 
while'knee  braces  are  used  to  stiffen  the  connections  of  the  intermediate 
trusses  to  the  columns.     Angles  are  used  as  diagonals  in  the  plane  of 
the  bottom  chords  of  the  roof  trusses,  and  in  the  vertical  sway  bracing 
between  columns,  both  on  the  sides  and  on  the  ends.     Rods  are  used 
as  diagonals  in  the  planes  of  the  top  chords  of  the  trusses,  and  in  the 
sides  and  the  tops  of  the  monitors.     The  end  panels  of  the  building  are 
usually  fully  braced  in  all  these  planes.     See  Fig.   156.     Only  every 
third  or'  fourth  intermediate  panel  is  similarly  braced  with  diagonals 
although  the  struts  extend  the  full  length  of  the  building.     The  struts 
in  the  braced  panels  are  usually  heavier  than  those  in  the  unbraced 
panels.     In  the  plane  of  the  bottom  chords  additional  diagonals  are  so 
placed  as  to  form  a  large  system  of  cross  bracing  which  extends  the 
full  width  of  the  building.     Vertical  bracing  is  sometimes  used  between 
trusses  at  the  center. 

6.  Fig.  140  shows  the  bottom  chord  bracing  and  the  end  sway  bracing 
for  the  mill  building  represented  in  Fig.  156.     The  working  lines  are 


140 


PART   II  —  STRUCTURAL   DRAFTING 


1  —  F 

24-4" 

1 
07 

79-O" 

08 

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4-3" 


Kl 


RIVETS  $ 


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D/AGOHALS 

Dl 

4 

_ 

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4 

„ 

D3 

3 

H 

D4 

3 

OS 

3 

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D6 

4 

D7 

4 

T/ES 

08 

2 

D/AGO/VALS 

D/2K 

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_ 

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DI3L 

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D/4 

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STRUTS 

SI 

2 

S7» 

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to 

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K/» 

10 

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Ml 

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M2 

4 

M3 

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M4 

Spacing  notff/ven  •  2% 


BRACf/VG 
rt/RMCE  BU/LD//VG 
MfTROPOL/TAIVSTttL  CO, 

BOSTON,  MASS. 

UNIVERSITY  BRIDGE  COMPANY 

WORCESTER  PLANT 

1776 


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WASHCRS  24*  J 


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Fig.  140.   Typical  Bracing  for  a  Mill  Building. 


CHAPTER  XXIII 


BRACING  SYSTEMS 


141 


referred  to  the  working  lines  of  the  trusses  and  columns  for  convenience 
in  checking  the  field  connections.  The  working  lines  through  the  end 
holes  of  the  diagonals  are  placed  to  make  the  clearances  on  each  side 
approximately  equal,  as  explained  on  page  77  : 1.  The  main  dimensions 
of  the  diagonals  between  end  holes  are  made  less  than  the  calculated 
distances,  as  explained  on  page  139  : 1.  For  the  sake  of  appearance,  the 
corners  of  all  plates  should  be  concealed  by  the  angles.  They  should 
preferably  be  made  to  fall  at  the  edges  of  single  angles,  but  this  is  not  of 
sufficient  importance  to  justify  any  increase  in  the  size  of  the  plate. 
The  comers  of  diagonal  cuts  can  be  shown  at  the  edges  of  angles  drawn 
in  position,  or  dimensions  can  be  given  if  the  angles  are  not  in  place. 
On  account  of  the  difficulty  of  holding  narrow  plates  in  the  shears  while 
long  diagonals  are  being  cut,  the  corners  of  splice  plates  such  as  pa 
or  pb  are  often  cut  at  45°  instead;  these  cuts  are  shown  but  not 
noted. 

1.  Unsymmetrical  bracing  is  illustrated  by  the  end  sway  bracing  of 
Fig.  140.  The  bottom  strut  S  7  connects  to  the  flange  of  the  channel 
of  C  1  (Fig.  135).  The  roof  truss  serves  as  the  top  strut,  the  bracket  at 
the  top  of  D  13  being  connected  both  to  the  truss  and  the  column;  note 
that  the  angle  which  connects  to  the  truss  is  cut  to  clear  the  fillet  of  the 
angle  ma  (Fig.  116).  After  the  working  points  have  been  located,  the 
length  and  the  slope  of  each  diagonal  can  be  found  in  the  usual  man- 
ner. The  position  of  the  intersection  of  the  diagonals  relative  to  the 
lower  working  points  can  be  found  by  solving  the  triangle  of  which 
these  three  points  are  the  vertices.  The  angles  may  be  easily  determined 
and  the  horizontal  side  is  known.  The  remaining  sides  may  be  found 
by  equating  the  ratios  of  the  sides  to  the  sines  of  the  opposite  angles. 
For  example,  the  angles  are  determined  from 'their  cotangents  as  fol- 
lows: 

log  14'  5|"  =  1 . 15949  log  15'  4f"  =  1 . 18740 

log  21'  2\"  =  1.32651  log  21'  6£"  =  1 . 33328 

log  cot      =9.83298  log  cot      =9.85412 

angle  =  55°  45'  angle  =  54°  27' 

third  angle  =  69°  48'  =  180°  -  55°  45'  -  54°  27' 

The  remaining  sides  are  found  as  follows: 


log  14'  51"  =  1 . 15949  log  14'  51"  =  1 . 15949 

log  sin  55°  45'  =  9.91729  log  sin  54°  27'  =  9.91041 

colog  sin  69°  48'  =  0.02757  colog  sin  69°  48'  =  0.02757 

1 . 10435  1 . 09747     . 

length  =  12'  8|"  length  =  12'  6ft" 

These  lengths  should  be  reduced  by  TV"  because  the  total  lengths  have 
been  shortened  f  "  to  insure  tightness  (page  139  : 1). 

2.  K  1  is  a  typical  knee  brace  to  connect  a  crane  girder  to  a  column. 
Two  types  of  connection  are  shown,  one  at  the  top  and  the  other  at  the 
bottom;  note  that  in  each  type  the  line  of  action  falls  well  within  the 
group  of  rivets  (page  138  :  4). 

3.  Typical   bottom   lateral   bracing   for  a   through   girder   bridge  is 
shown  in  Fig.  142.     The  plates  are  connected  both  to  the  girders  and 
to  the  floor  beams.     Small  angles  ma  are  used  to  connect  the  diagonals 
to  the  bottom  flange  angles  of  the  stringers;  this  is  done  to  prevent  longi- 
tudinal movement  of  the  stringers  due  to  traction  and  braking  stresses. 
The  bottom  lateral  bracing  of  a  truss  bridge  is  similar  to  that  of  the 
girder  bridge  except  that  it  is  usually  made  heavier  because  of  the  in- 
creased span.     The  single  angles  are  often  replaced  by  double  angles. 

4.  The  top  lateral  system  of  a  through  truss  bridge  cannot  be  made 
a  complete  system  of  cross  bracing  extending  down  the  inclined  end 
posts  to  the  supports  because  a  clear  passageway  must  be  maintained 
at  the  ends  of  the  bridge.     Cross  bracing  is  used  in  each  panel  of  the 
main  top  chord,  but  a  portal  strut  is  used  to  transmit  the  corresponding 
stresses  to  the  end  posts  which  act  as  girders  in  carrying  these  stresses 
to  the  supports.     The  portal  struts  and  the  intermediate  struts  or  sway 
braces  are  made  as  deep  as  the  required  clearance  will  allow;  in  general 
they  are  made  much  heavier  than  they  were  a  few  years  ago,  to  give 
greater  rigidity,  particularly  in  railway  bridges.     The  intermediate  sway 
braces  are  usually  made  of  four  angles  latticed,  as  SB  1,  Fig.  143;  more 
elaborate  bracing  is  used  in  bridges  with  inclined  top  chords  because  of 
the  greater  depth  available.     Many  different  types  of  portal  struts  are 
used,  as  for  example  the  solid  web  type,  PS  1,  Fig.  143,  or  the  latticed 
type,  Fig.  149.     Since  the  portal  strut  is  in  an  inclined  plane,  the  outer 
angle  at  the  bottom  forms  a  trough  which  should   be  provided  with 


142 


PART  II  —  STRUCTURAL  DRAFTING 


BRACfNG 
TYP/CAL  GIRDER  BR/DGES 


Fig.  142.  Typical  Bracing  for  a  Girder  Bridge. 


CHAPTER  XXIII 


BRACING   SYSTEMS 


143 


0  4S6-2V"  4i43,4   5@6-2-6" 


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UNIVERSITY  BRIDGE  COMPANY 

AMBRIDGE PLANT 

26 


IN  CHARGE  OF  

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,H,K.DBY   H.D.I.    "/e/I4 


Fig.  143.  Typical  Top  Lateral  Bracing  for  a  Railroad  Truss  Bridge. 


144 


PART   II  —  STRUCTURAL  DRAFTING 


drain  holes  to  prevent  the  accumulation  of  water.  The  corners  of  some 
of  the  angles  of  a  portal  may  be  cut  at  45°  if  the  appearance  is  improved 
thereby.  The  intermediate  top  struts  or  sway  braces  can  usually  be 
made  deeper  than  the  top  chords;  lattice  angles  are  used  when  the 
depth  is  too  great  for  the  use  of  lattice  bars.  The  connection  plates 
at  the  ends  (pf)  must  be  cut  out  to  clear  the  angles  of  the  top  chords; 
this  is  one  of  the  few  places  where  reentrant  cuts  are  used.  Such  cuts 
are  usually  made  by  punching  a  series  of  connected  holes  the  same  size 
as  the  rivet  holes,  and  then  chipping  off  the  remaining  points  with  a 
pneumatic  chisel.  A  small  curve  is  drawn  at  the  vertex  of  the  reentrant 
angle  to  shdw  that  it  is  unnecessary  to  chip  out  the  extreme  corner  to 
form  a  right  angle.  The  top  laterals  or  diagonals  are  composed  of  one 
or  two  angles  in  the  lighter  bridges  and  two  or  four  angles  latticed  in 
the  heavier  bridges.  The  latticed  members  connect  to  plates  which 
are  fastened  to  the  tops  and  the  bottoms  of  the  chords;  the  depth  is 
thus  determined  by  the  depth  of  the  chord  members,  being  made  V/'  or 
j"  less  than  the  clear  distance  between  the  lateral  plates.  The  upper 
lateral  plates  which  serve  to  cover  joints  in  the  chords  extend  the  full 
width  of  the  chords;  other  plates  connect  to  the  inner  side  only.  Plate 
P  6  connects  to  the  chord  U  1-3  (Fig.  124),  and  to  the  top  of  SB  1. 
P  7  connects  to  the  upper  face  of  the  angle  on  the  bottom  of  the  chord 
and  to  the  vertical  plate  of  SB  1.  The  diagonals  fit  between  these 
plates.  Plate  P  4  connects  to  the  top  of  the  chord  and  it  is  bent  up  to 
connect  to  the  top  angle  of  the  portal  strut  PS  1.  The  holes  in  the  bent 
up  portion  should  appear  as  ellipses  instead  of  circles,  but  on  account  of 
the  difficulty  in  drawing  small  ellipses,  circles  are  sometimes  used  when 
no  misunderstanding  is  likely  to  result.  P  5  connects  to  the  bottom 
angle  of  the  top  chord,  to  the  vertical  face  of  the  end  post,  and  to  the 
end  plate  of  the  portal  strut  PS  1.  The  angles  on  this  bent  plate  are 
not  shown  in  true  projection  because  the  drawing  would  be  made  un- 
necessarily complicated.  The  bend  in  the  plate  is  clearly  shown  and 
dimensioned.  If  the  holes  in  the  angles  mb  were  to  be  shown  accu- 
rately as  circles  two  additional  views  would  be  required.  It  seems 
equally  clear  and  more  convenient  to  draw  the  top  view  of  the  angles 
directly  above  the  elevation  and  to  show  them  conventionally  by  three 
lines  to  facilitate  dimensioning  the  rivets  and  holes;  confusion  would 


result  if  both  the  rivets  and  the  holes  were  shown  in  this  view  in  exact 
orthographic  projection.  Care  should  be  taken,  however,  to  give  dimen- 
sions only  in  the  views  where  the  corresponding  distances  are  shown  in 
true  projection. 

1.  Brackets.  —  The   compression   chords   of  bridges   where  no   top 
laterals  can  be  used  must  be  braced  in  some  other  way  to  give  inter- 
mediate support  to  the  compression  members  to  prevent  them  from  buck- 
ling.    "Pony  trusses  "  are  trusses  which  are  not  deep  enough  to  permit 
the  use  of  overhead  bracing.     They  may  be 

braced  by  means  of  brackets  such  as  that 
shown  in  Fig.  144.  Similarly,  the  compres- 
sion flanges  of  through  plate  girder  railroad 
bridges  are  braced  transversely  by  means  of 
brackets  or  deep  gusset  plates  at  the  con- 
nections of  the  floor  beams  to  the  girders,  as 
shown  in  Fig.  99.  Through  plate-girder 
highway  bridges  are  braced  in  much  the 
same  manner  except  that  it  is  impractical  to 
use  as  wide  plates  on  account  of  the  en- 
croachment upoij  the  clear  roadway.  The 
narrower  plates  are  sometimes  supplemented 
by  other  plates  or  brackets  on  the  outside 
of  the  girders. 

2.  Deck  plate  girder  bridges  are  braced 
vertically  by  means  of  cross  frames  such  as 
shown  in  Fig.  142.     The  frames  at  the  ends 

of  the  bridges  (CF  1)  are  made  heavier  than  the  intermediate  ones  (CF  2). 
The  cross  frames  are  connected  to  the  stiffening  angles  of  the  girders  and 
also  to  the  plates  of  the  lateral  bracing  which  are  attached  to  the  under 
sides  of  the  top  flanges.  The  key  plan  in  Fig.  142  shows  a  typical  layout 
of  the  lateral  bracing,  single  angles  being  used  for  the  diagonals  and  also 
for  the  struts  between  the  cross  frames.  This  lateral  bracing  is  often 
drawn  on  the  sheet  with  the  girders  so  that  the  connection  plates  can 
be  shown  in  position,  in  order  to  save  the  duplication  of  many  of  the 
dimensions.  The  spacing  of  the  holes  in  the  cross  frames  and  the  stiffen- 
ing angles  should  be  so  arranged  that  a  clearance  of  A"  is  allowed 


CHAPTER  XXIII 


BRACING  SYSTEMS 


145 


between  the  tops  of  the  cross  frames  and  the  lateral  plates;  in  case  the 
cross  frames  connect  to  bottom  lateral  plates  as  well,  A"  clearance  is 
allowed  at  the  bottom  and  5"  at  the  top. 

1.  The  wind  bracing  of  an  office  building  depends  upon  so 
many  factors  that  it  is  impossible  to  discuss  it  comprehensively 
here.*  The  form  of  the  building,  the  number  of  floors,  the  number 

*  See  Fleming's  "Six  Monographs  on  Wind  Stresses,"  Kirkham's  "Structural  En- 
gineering," or  Ketchum's  "Structural  Engineers'  Handbook,"  all  published  by  McGraw- 


and  the  position  of  the  partitions,  and  the  position  of  the  doors  and 
windows,  are  points  to  be  considered  in  selecting  the  form  of  bracing. 
Diagonal  bracing,  portal  bracing,  knee  bracing,  and  brackets  are  the  more 
common  types.  Typical  brackets  for  connecting  office-building  beams 
and  girders  to  columns  are  illustrated  in  Fig.  145. 


Hill  Book  Co.  Inc.,  New  York;  also  Burt's  "Steel  Construction,"  American  Technical 
Society,  Chicago. 


Fig.  145. 


CHAPTER  XXIV 
MISCELLANEOUS  FRAMING 

SYNOPSIS:  Girts,  struts,  plate  work,  and  skew  work. 


1.  Illustrative  Drawings.  —  In  this  chapter  are  given  a  few  miscellane- 
ous drawings  to  supplement  those  of  the  preceding  chapters.     Taken  as 
a  whole,  the  drawings  in  this  book  have  been  chosen  to  illustrate  different 
types  of  members  and  different  methods  of  detailing.     No  attempt  has 
been  made  to  show  the  working  drawings  of  complete  structures,  although 
in  some  cases  several  different  members  of  the  same  structure  are  shown. 
It  is  felt  that  there  are  enough  drawings  to  illustrate  the  fundamentals  of 
structural  drafting,  and  at  the  same  time  to  show  many  of  the  more 
common  kinds  of  connection. 

2.  In  Fig.  147  are  shown  some  of  the  girts  and  struts  of  the  mill  build- 
ing of  Fig.  156.     F  7  and  F  8  are  typical  intermediate  side  and  end  girts, 
with  holes  in  the  outstanding  legs  for  bolting  the  window  frames  in  posi- 
tion.    The  side  girts  in  the  end  panels  are  the  same  as  in  the  intermediate 
panels,  but  the  end  girts  which  connect  to  the  corner  columns  are  made 
long  enough  to  support  both  the  side  and  the  end  corrugated  steel  at  the 
corners.     Thus  F  9  is  an  end  girt  which  connects  to  the  inside  face  of  the 
outer  angles  of  column  C  1  (Fig.  135),  and  extends  beyond  the  column 
until  it  is  flush  with  the  outer  edge  of  the  side  girts.     If  possible  the  con- 
nections for  these  end  girts  are  made  so  that  the  holes  in  the  corner 
columns  are  spaced  the  same  as  in  the  intermediate  columns;    this  not 
only  simplifies  the  drafting  and  the  shop  work  but  it  also  facilitates  future 
extension  of  the  building.     F  10  is  an  intermediate  support  for  the 
louvres;  it  connects  to  the  purlins  which  are  attached  to  the  side  of  the 
monitor  (Fig.  117)  as  indicated  in  the  side  elevation,  Fig.  156.     If  5  is  a 
hanger  or  sag  bar  which  is  used  in  place  of  a  sag  rod  to  support  a  long  girt 
wherever  a  window  prevents  the  use  of  a  rod. 


3.  S  2  and  S  3  are  typical  eave  struts ;    they  serve  as  girts  and 
purlins  to  support  the  corrugated  steel,  as  well  as  struts  for  three  differ- 
ent systems  of  bracing  (page  138  :  3).     Each  channel  is  stiffened  by  an 
angle  which  extends  the  full  length  between  the  connection   plates. 
Holes  are  provided  in  S  2  for  the  sway  bracing  which,  at  the  bottom, 
connects  to  the  strut  S  4  shown  below.     S  4,  S  5  and  S  6  are  typical 
two-angle  struts  used  in  the  sides  and  the  ends  of  the  building;  they  serve 
also  as  girts. 

4.  Fig.  148  shows  a  drawing  of  some  of  the  steel  plates  of  a  roof  for  a 
cast  house  around  a  blast  furnace.     This  is  not  as  common  an  application 
of  plate  work  as  floor  plates  or  the  plates  in  a  tank,  but  in  simple  form  it 
illustrates  the  method  of  dimensioning.     In  tank  work  the  rivets  must  be 
placed  closer  together  and  the  outer  edges  of  the  overlapping  plates  must 
be  beveled  for  calking,  in  order  to  make  the  joints  watertight  (page 
69  :  1). 

5.  Skew  Work.  —  Some  of  the  connections  encountered  in  structural 
work  require  more  than  ordinary  computation  in  determining  the  proper 
angles  and  dimensions.     Common  examples  of  this  class  of  work  are  hip 
and  valley  roof  construction,  skew  portal  bracing,  bins,  chutes,  hoppers, 
etc.     The  details  and  the  corresponding  calculation  for  the  construction 
of  different  types  of  intersecting  roofs  have  been  so  fully  treated  by  the 
author  in  another  volume  *  that  they  are  not  even  summarized  here.     A 
complete  mastery  of  that  book  should  enable  the  draftsman  to  apply  the 
principles  to  the  solution  of  other  problems  of  a  similar  nature.     On« 
form  of  skew  portal  is  illustrated  in  Fig.  149;  it  is  designed  to  connect  tc 

*  "Hip  and  Valley  Rafters,"  John  Wiley  and  Sons,  Inc.,  New  York. 


146 


CHAPTER  XXIV 


MISCELLANEOUS  FRAMING 


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GIRTS,  STRUTS  ETC. 

FURNACE  BUILDING 

METROPOLITAN  STEEL  CO. 

BOSTON,  MASS. 

UNIVERSITY  BRIDGE  COMPANY 

,   Worcester    PLtNT 

IN  CHARGE  ne        M.  G.  0. 

MADE  nv     i.S.D,  S/  IS/I  a     f>         1776 


CH.K.0 


Fig.  147.  Typical  Girts  and  Struts  for  a  Mill  Building. 


148 


PART  II  —  STRUCTURAL  DRAFTING 


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Fig.  148.  Steel  Roof  Plates. 


CHAPTER  XXIV 


MISCELLANEOUS   FRAMING 


149 


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BRIDGE  OVER  MILL  RIVER 
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fl/EWHAVCN,  C01W. 

UNIVERSITY  BRIDGE  COMPANY 
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Fig.  149.   Portal  Bracing  for  a  Skew  Bridge. 


150 


PART  II  —  STRUCTURAL  DRAFTING 


the  cover-plate  faces  of  the  end  posts.  There  are  only  two  angles  to  be 
determined  which  involve  the  use  of  angles  in  more  than  one  plane;  these 
are  the  angle  of  bend  (B)  and  the  skew  angle  (P)  in  the  plane  of  the  portal. 
Formulas  for  these  angles  are  shown  in  Fig.  150  in  terms  of  the  truss  angle 

(T)  and  the  skew  angle  (H) 
in  a  horizontal  plane.*  The 
use  of  these  formulas  is  illus- 
trated by  the  determination  of 
these  angles  in  the  portal  of 
Fig.  149,  using  the  following 
data: 

22'  2§"  =  the  panel  length  of 
the  truss. 

29'  0"     =  the  panel  depth  of 
the  truss. 

16'  5"     =  the  distance  c.   to 

c.  of  trusses. 

9'  0"  =  the  lead  of  one  truss 
in  advance  of 
the  other,  or  the 
amount  of  skew, 
measured  paral- 
lel to  the  axis  of 
the  bridge. 

14'  4"     =  16'  5"  -  2(1'0£")  the  distance  c.  to  c.  of  working  points 
measured  at  right  angles  to  the  axis  of  the  bridge. 

*  For  other  angles  see  Conklin's  "Structural  Steel  Drafting,"  John  Wiley  and  Sons, 
Inc.,  New  York;  Turner's  articles  in  Vol.  43  of  the  Engineering  News;  or  Dannen- 
berg's  diagram  in  the  Engineering  Record,  Feb.  17,  1912. 


FORMULAS 
sin  P-sin  H  sin  T 
tan  B-tan  B  c&a  T 


Fig.  150. 


The  functions  of  the  truss  angle  (T)  and  the  skew  angle  (H)  are  found  as 
follows: 


log  22' 2-|"  =  1.34652 
log  29'  0"  =  1.46240 
log  tan  T 
log  sin  T 


log    9'0"  =  0.95424 
log  14'  4"  =  1 . 15635 


=  9.88412 
=  9.78390 
=  9.89978 


log  tan  H   =  9.79789 
log  sin  H   =  9.72572 
log  cos  T 

From  sin  P  =  sin  H  sin  T,  log  sin  H  =  9 . 72572 

log  sin  T  =  9.78390 
log  sin  P  =  9.50962 

whence  the  skew  in  the  plane  of  the  portal  has  a  slope  of  4|-  in  12. 

From  tan  B  =  tan  H  cos  T,  log  tan  H  =  9 . 79789 

log  cos  T  =  9.89978 
log  tan  B  =  9.69767 

whence  the  bend  in  the  plate  is  6  in  12. 

The  distances  6'  Of"  and  6'  2"  are  determined  by  the  allowed  clear- 
ance; by  multiplying  them  by  tan  P  the  distances  2'  Of"  and  2'  1J"  an 
found.  The  working  points  of  the  upper  and  lower  ends  of  the  diagonal; 
are  located  so  that  the  horizontal  panel  lengths  are  equal.  The  tw( 
different  lengths  of  diagonals  from  center  to  center  of  end  rivets  may  b( 
calculated  in  the  usual  manner  after  the  proper  horizontal  distanci 
between  the  end  rivets  of  each  diagonal  has  been  found.  The  rivet  spac 
ing  in  the  top  chord  from  left  to  right  should  be  made  the  same  as  thi 
spacing  in  the  bottom  chord  from  right  to  left,  in  order  to  make  th' 
plates  and  angles  interchangeable. 

1.  Eye  bars,  rods,  and  miscellaneous  material  are  usually  shown  01 
special  printed  forms  or  else  drawn  on  combination  sheets,  as  explains 
on  page  174  :  2. 


CHAPTER  XXV 
ERECTION   PLANS   AND   DIAGRAMS 

SYNOPSIS:  Outline  or  skeleton  drawings  are  made  to  represent  a  portion  or  the  whole 
of  a  structure  to  show  the  relation  of  the  different  members,  and  how  these  members 
are  to  be  assembled  at  the  site.  The  identification  mark  of  each  member  is  indicated 
upon  the  diagram  for  the  use  of  the  draftsman,  the  erectors,  and  others.  The  dia- 
grams may  be  used  also  as  progress  record  sheets. 


1 .  The  plans  and  diagrams  of  a  proposed  structure  serve  as  keys  to  the 
structure.     General  dimensions,  identification  marks,  and  other  informa- 
tion regarding  the  structure  as  a  whole  are  thus  presented  to  the  drafts- 
men, the  shopmen,  the  inspectors,  the  erectors,  and  the  contractors  for 
allied  work.     The  diagrams  are  usually  prepared  as  soon  as  possible  after 
the  design  sheets  are  received  in  the  drafting  room.     In  some  classes  of 
work  they  cannot  be  completed  until  later,  but  the  main  outline  is  pre- 
pared and  the  missing  dimensions  and  identification  marks  are  added  as 
the  detailed  drawings  are  made.     Each  member  is  usually  represented 
by  a  single  heavy  line.     These  lines  are  not  drawn  far  enough  to  intersect, 
but  spaces  are  left  to  indicate  the  extent  of  each  member.     Often  typical 
connections  are  shown  on  the  diagrams.      This  insures  greater  uni- 
formity when  the  drawings  are  made  by  several  draftsmen  and  enables 
the  engineers  who  approve  the  drawings  to  approve  the  types  of  con- 
nections before  they  have  been  incorporated  extensively  on  the  detailed 
drawings. 

2.  The  draftsmen  who  make  the  working  drawings  obtain  their  in- 
formation largely  from  the  diagrams  which  are  prepared  in  the  drawing 
room,  although  they  must  supplement  this  information  by  data  from  the 
design  sheets  and  from  other  available  sources.     As  each  working  draw- 
ing is  completed  the  draftsman  should  make  sure  that  the  identification 
marks  are  properly  placed  upon  the  diagrams.     If  the  marks  have  been 
put  on  by  another  person  he  should  verify  them.     These  marks  should 


also  be  checked  by  the  person  who  checks  the  corresponding  working 
drawing. 

3.  The  erector  uses  the  diagrams  as  a  guide  in  assembling  the  different 
members  in  the  field.     For  this  purpose  not  only  should  every  identifica- 
tion mark  be  shown,  but  sufficient  notes  and  sketches  should  be  added  to 
insure  the  proper  erection. 

4.  Diagrams  must  be  prepared  to  give  necessary  information  to  other 
contractors  who  construct  parts  of  the  same  structures  or  connecting 
structures.     Thus  a  foundation  plan  must  be  drawn  for  the  contractor 
who  builds  the  foundations.     A  data  sheet  or  crane  clearance  diagram 
must  be  prepared  for  the  contractor  who  builds  the  traveling  cranes  for 
a  building.     This  is  usually  based  upon  similar  diagrams  or  upon  charts 
furnished  by  crane  manufacturers,  but  a  new  diagram  is  made  for  each 
structure  and  submitted  to  the  crane  manufacturer  for  approval  to  make 
sure  that  ample  clearance  is  provided  for  the  crane.     Similarly,  special 
data  sheets  may  be  required  in  order  that  proper  provision  may  be  made 
for  machinery  or  shafting.     Such  data  sheets  may  be  made  either  by  the 
structural  draftsman  or  by  the  draftsman  of  the  company  which  furnishes 
the  machinery. 

5.  The  diagrams  of  simple  structures  may  be  combined  on  a  single 
sheet,  but  as  the  number  of  members  shipped  separately  increases,  the 
diagrams  become  more  complex  and  many  sheets  may  be  required.     A 
list  of  all  the  drawings  on  a  contract  is  usually  placed  upon  one  of  these 


151 


152 


PART   II  —  STRUCTURAL  DRAFTING 


sheets.  Typical  plans  and  diagrams  for  different  classes  of  work  are 
illustrated  below.  A  careful  study  of  these  diagrams  should  be  made. 
They  may  serve  as  a  guide  when  similar  diagrams  are  being  drawn  for 
the  first  time. 

1.  Plate-girder  bridges  of   single  span    may  usually  be  completely 
represented  by  one  diagram.     Such  a  diagram  for  a  through  bridge  is 
shown  in  Fig.  153.     The  plan  of  anchor  bolts  is  shown  at  the  bottom,  a 
partial  elevation  with  important  dimensions  is  shown  near  the  middle  of 
the  sheet,  while  the  plan  of  the  bridge  at  the  top  of  the  sheet  shows  the 
relative  position  of  the  girders,  the  floor  system,  and  the  lateral  bracing. 
In  this  simple  structure  all  the  marks  appear  upon  the  plan  which  would 
therefore  be  sufficient  for  the  erection  of  all  the  steel  work.     The  more 
detailed  elevation  is  added,  however,  in  order  to  show  the  relative  ele- 
vations clearly  so  that  the  foundations  may  be  placed  at  the  proper 
distance  below  the  base  of  rail. 

2.  The  erection  diagram  for  the  steelwork  of  a  truss  bridge  is  shown  in 
Fig.  154.     In  bridge  work  the  far  truss  is  shown  in  the  elevation,  the 
members  in  the  left  half  being  detailed  in  the  working  drawings.     These 
members  are  consequently  marked  "right  "  when  "rights  "  and  "lefts  " 
are  required  (page  81 : 2).  A  combined  cross-section  and  end  view  is  drawn 
in  sufficient  detail  to  show  the  main  dimensions  and  the  relative  eleva- 
tions of  the  abutments,  the  floor  beams,  the  stringers,  and  the  rails.     In 
the  plan  of  the  floor  system,  portions  of  the  single-angle  diagonals  between 
the  stringers  are  shown  in  a  typical  panel  to  indicate  which  way  the  angles 
are  to  be  erected. 

3.  A  simple  anchor-bolt  plan  for  a  mill  building  is  shown  in  Fig.  155. 
From  this  plan  the  contractor  for  the  foundations  can  determine  the 
number  and  the  location  of  the  piers  which  support  the  columns,  the  sizes 
of  the  corresponding  column  base  plates  and  the  column  loads,  the  sizes 
and  the  spacing  of  the  anchor  bolts  and  the  distances  they  are  to  be 
imbedded  in  the  masonry.     Dimensions  to  the  extreme  exterior  of  the 
building  (in  this  case  corrugated. steel)  are  also  given.     The  list  of  anchor 
bolts  and  washers  which  the  contractor  must  set  is  summarized.     This 
furnace  building  is  left  open  all  around  for  about  10  feet  from  the  ground 
(see  Fig.  156)  and  hence  no  doors  are  required.     Small  piers  for  door 
posts  would  be  indicated  upon  the  plan  and  the  door  posts  shown  in  detail 


much  as  the  columns  are  shown.  Usually  the  small  swedge  bolts  for 
door  posts  are  placed  after  the  steelwork  is  in  position.  A  note  to  this 
effect  should  appear  near  the  enlarged  detail  of  the  bolts.  A  note  ex- 
plaining who  furnishes  and  sets  the  anchor  bolts  should  be  given  unless 
uniform  practice  makes  such  a  note  unnecessary. 

4.  A  typical  erection  diagram  for  a  mill  building  is  shown  in  Fig.  156; 
several  typical  detailed  drawings  for  this  same  building  have  already  been 
shown.     For  larger  or  more  complicated  buildings  more  than  one  sheet 
would  be  required,  the  plan  of  the  roof  and  the  elevations  being  placed 
on  one  sheet  and  the  other  plans  on  another  sheet.     This  is  particularly 
necessary  when  elevations  of  both  sides  and  perhaps  both  ends  are  re- 
quired.    Note  that  portions  of  the  girts  are  shown  near  a  corner  of  the 
building  to  indicate  whether  the  vertical  legs  are  turned  up  or  down; 
they  are  usually  turned  down  except  over  windows,  doors,  or  other  open- 
ings.    The  column  marks  are  repeated  in  the  different  views  for  the  con- 
venience of  the  draftsmen  and  others  who  wish  to  find  the  drawing  of 
the  column  which  shows  what  provision  has  been  made  for  the  connection 
of  any  specific  member. 

5.  A  crane  clearance  diagram  for  the  same  mill  building  is  shown  in 
Fig.  157.     This  shows  the  crane  manufacturers  just  how  much  space  is 
available  for  the  crane  and  its  appurtenances  (see  above). 

6.  Special  erection  diagrams  are  usually  drawn  for  corrugated  steel. 
These  diagrams  show  the  position  of  the  sheets  of  different  lengths  and 
show  how  some  of  them  are  beveled  in  the  field  for  the  gable  ends. 
Typical  details  are  drawn  to  show  the  arrangement  of  the  corrugated 
steel  and  the  flashing  at  corners,  windows,  doors,  cornices,  ventilators, 
etc.     These  diagrams  are  usually  drawn  by  experienced  men,  and  it  does 
not  seem  advisable  to  devote  sufficient  space  in  this  book  to  treat  the 
subject  as  fully  as  it  should  be  treated,  if  at  all.* 

7.  A  portion  of  a  typical  floor  plan  of  an  office  building  is  shown  in 
Fig.  158.     An  experienced  draftsman  can  usually  make  the  plans  of 
office  buildings  quite  complete.     He  can  determine  the  lengths  of  all 
main  material  and  he  can  anticipate  the  details  with  sufficient  accuracy 
to  assign  identification  marks  to  all  beams  and  girders,  making  sure 

*  For  typical  plans  and  details  see  either  Ketchum's  "Mill  Buildings,"  or  Ketchum's 
"Structural  Engineers'  Handbook,"  McGraw-Hill  Book  Co.,  Inc.,  New  York. 


CHAPTER  XXV 


ERECTION   PLANS  AND  DIAGRAMS 


153 


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3 

Laterals,  etc* 

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MASONRY  AND  ERECTION  DIAGRAM 

70  FT.  S.  T.  THRU.  PLATE  GIRDER  SPAN 

NA  TIONAL  RAIL WA  Y  CO. 

NEW  HAVEN  CONN. 

UNIVERSITY  BRIDGE  COMPANY 

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N  CHARGE  OF     C.T.B.  n        1918 


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CH,K,D  nv     J.C.  4/10/18 


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Fig.  153.   Masonry  and  t  rection  Diagram  for  a  Railroad  Girder  Bridge. 


154 


PART   II  —  STRUCTURAL  DRAFTING 


EXPANSION 


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ERECTION  DIAGRAM 
I60FT.S.T.  THRU.  TRUSS  BRIDGE 
MASSACHUSETTS  R.R. 

BOSTON,  MASS. 

UNIVERSITY  BRIDGE  COMPANY 


For  Each  Shoe:-4$wedge  Bolrsll*2-l " 
4-Wasfiers  4>i  ©  ,, 
4-C.P.Seps.lf  *7rj 


Fig.  154.  Erection  Diagram  for  a  Railroad  Truss  Bridge. 


CHAPTER  XXV 


ERECTION  PLANS  AND  DIAGRAMS 


155 


4  Anchor  Roqtl-t"rf  4-3' 
4  Wishej-s  8'X-i  xg 


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Anchor  bolts  furnished  but  not  set  by  Univ.  Bridge  Co. 


LIST  OF  ANCHORS 


48 


Anchor  Rods 


Sweage  Bolts 


ANCHOR  BOLT  PLAN 

FURNACE  BUILDING 

METROPOLITAN  STEEL  CO. 

BOSTON,  MASS. 

UNIVERSITY  BRIDGE  COMPANY 

Worcester^ PLANTi 

1778 


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Fig.  155.  Anchor-bolt  Plan  for  a  Mill  Building. 


156 


PART   II  —  STRUCTURAL  DRAFTING 


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Fig.  156.   Erection  Diagram  for  a  Mill  Building. 


CHAPTER  XXV 


ERECTION  PLANS  AND  DIAGRAMS 


157 


DRAFTING  FORM  4 

UNIVERSITY    BRIDGE       COMPANY 

WORCESTER            BHAM^M 

FURNACE  BUILDING                                  DBAWIMC  or    CRANE  CLEARANCE  DIAGRAM 

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MADE  BY                       J'T.C.               B.TE            7-IS-I9I8          CONTRACT  NO                  1*78 

CHECKED  BY                f.C.f.              pATE            7-IS-I9I8           SHEET  NUMBER             f  F  ' 

Fig.  157.  Crane  Clearance  Diagram. 


that  beams  which  are  alike  are  marked  alike,  and  conversely  that  no 
beams  are  marked  alike  unless  they  are  interchangeable.  The  columns 
are  numbered  consecutively,  no  two  bearing  the  same  number  (see 
page  81  :  5).  Typical  connections  may  be  shown  on  the  diagrams. 
The  advantages  of  having  the  plans  carefully  and  completely  made  at 
the  outset  are  many.  First,  the  material  order  bills  may  be  made  with 
more  assurance  than  if  ordered  from  the  design  sheets  without  identi- 
fication numbers.  Secondly,  the  plans  may  be  sent  for  approval  at 
once  and  the  main  dimensions,  typical  connections,  and  special  wall 
details  may  thus  be  approved  before  they  have  been  incorporated  in  so 
many  detailed  drawings  that  any  change  would  necessitate  excessive 
alterations.  Thirdly,  if  any  necessary  information  is  lacking  the  fact 
is  usually  discovered  in  time  to  obtain  the  complete  data  before  it  is 
needed.  Fourthly,  the  making  of  the  working  drawings  for  the  beams 
becomes  routine  work  which  can  be  done  by  comparatively  inexperi- 
enced draftsmen  with  very  little  supervision. 

1.  Method  of  Procedure.  —  An  office-building  plan  is  drawn  in  about 
the  following  order.  First  the  column  centers  are  located  and  then  the 
column  sections  are  shown  conventionally.  Although  considerable 
work  is  involved  in  showing  each  column  it  seems  worth  while  to  indi- 
cate clearly  the  type  of  each  column  and  the  way  it  is  turned.  Next 
the  beams  may  be  drawn  and  the  corresponding  dimensions  recorded. 
All  openings  for  stairs,  elevators,  stacks,  etc.,  are  indicated  convention- 
ally by  light  diagonal  lines  so  that  no  floor  will  be  constructed  in  these 
spaces.  Tie  rods  are  indicated  wherever  they  are  required  to  resist  the 
thrust  of  the  floor  arches  as  indicated  upon  the  design  sheets  (see  page 
20  :  3).  Each  beam  section  may  now  be  billed  on  the  diagram.  Much 
repetition  may  be  avoided  through  the  use  of  the  abbreviation  "do  " 
for  "ditto  ";  ditto  marks  (")  should  never  be  used  because  they  are 
not  sufficiently  distinctive.  Care  must  be  taken  not  to  insert  any  other 
beam  section  between  "one  beam  section  and  a  corresponding  "do." 
The  diagram  should  show  clearly  the  way  the  flanges  of  channels  turn. 
This  may  be  done  by  means  of  small  sectional  views,  or  by  indicating  a 
portion  of  the  channel  flange.  A  more  convenient  method  is  to  turn  the 
channel  mark  (LJ)  to  indicate  which  way  the  flanges  face,  as  illustrated 
near  the  lower  left-hand  corner  of  Fig.  158  where  the  channels  numbered 


PART   II  —  STRUCTURAL  DRAFTING 


Fig.  158.  Partial  Floor  Plan  for  an  Office  Building. 


CHAPTER  XXV 


ERECTION  PLANS  AND   DIAGRAMS 


159 


59  and  61  are  billed.  The  relative  elevations  of  all  beams  and  tie  rods 
should  be  indicated.  A  general  sketch  may  be  drawn  for  most  beams, 
while  the  elevations  of  the  tops  of  exceptional  beams  above  or  below  the 
finished  floor  line  may  be  indicated  by  dimensions  in  parentheses.  The 
type  of  connections  for  beams  to  beams  and  beams  to  columns  should 
be  determined  and  preferably  shown  on  the  plan.  Since  the  lengths  of 
the  beams  which  connect  to  the  columns  depend  upon  the  sizes  of  the 
columns  it  is  convenient  to  place  near  each  column  small  figures  to  indicate 
the  distances  from  the  center  of  the  column  to  the  outer  faces.  Thus  for 
the  channel  columns  shown,  one  figure  gives  the  distance  from  the  center 
to  the  outer  face  of  the  channel  (constant  for  a  given  depth  of  channel), 
and  also  the  distance  from  the  center  to  the  outer  face  of  the  cover  plates 
(varies  with  the  thickness  of  the  plate  and  also  with  the  depth  of  chan- 
nel). After  these  figures  are  completed  and  the  type  of  connection 
determined,  the  length  to  be  ordered  may  be  placed  .on  each  beam. 
The  experienced  draftsman  can  now  quite  easily  assign  to  the  beams 
the  numbers  of  the  identification  marks.  The  floor  number  or  letter  of 
the  complete  identification  mark  (see  page  81  :  5),  is  given  once  for  all 
in  the  title  and  need  not  be  repeated  on  each  beam.  The  lengths  of 
tie  rods  should  be  indicated  on  the  plan.  Some  companies  assign  a 
letter  with  consecutive  numbers  to  the  rods,  as  X  1,  X  2,  etc.  A 
better  method  is  illustrated  in  the  plan  shown,  where  the  identification 
mark  in  the  circle  is  the  length  of  the  rod  in  inches.  See  page  82  :  3. 
It  is  unnecessary  to  mark  every  rod  on  the  plan  when  a  single  mark  be- 
tween continuous  lines  of  beams  will  suffice. 

1.  Plans  for  different  floors  may  be  combined  when  quite  similar. 
The  column  dimensions  and  beam  lengths  may  differ  but  these  differ- 
ences may  be  indicated  without  drawing  separate  plans.     Ordinarily, 
separate  plans  are  drawn  for  the  first  and  second  floors  and  the  roof, 

I  the  intermediate  floors  being  combined  in  a  single  plan. 

2.  A  column  schedule  is  often  prepared  for  use  in  the  drafting  room, 
ilthough  it  is  not  indispensable  to  the  erector.     One  form  of  column 
schedule  is  shown  in  Fig.  160.     One  space  is  laid  off  horizontally  for 
;ach  column,  and  the  story  heights  are  plotted  and  dimensioned  verti- 
•ally.     Heavy  lines  are  drawn  to  indicate  the  milled  ends  of  the  column 
sections  at  the  splices  and  at  the  extreme  bottoms.     The  line  at  the 


bottom  is  shown  broken,  when  the  column  bases  are  not  all  at  the  same 
elevation.  The  component  material  for  each  section  is  given,  and  also 
any  fillers  required  at  the  splices.  The  cap  plates  are  indicated  clearly 
by  shaded  spaces  so  that  the  proper  main  material  will  be  ordered  short 
to  allow  for  the  thickness  of  the  cap  plates.  The  reinforcing  plates 
may  be  given  just  below  the  cap  plates.  The  loads  or  the  column 
areas  are  sometimes  given,  but  this  is  usually  unnecessary.  If  one  whole 
column  from  basement  to  roof  is  like  another  in  section  and  in  length,  it 
may  be  referred  to  the  other  in  order  to  avoid  needless  duplication.  A 
typical  column  splice  is  often  shown  on  this  sheet  so  that  it  may  be 
approved  before  the  detailed  drawings  are  far  advanced.  The  column 
schedule  may  be  made  to  serve  as  an  index  to  the  drawings  upon  which 
the  different  columns  are  detailed;  the  drawing  number  may  be  placed 
at  the  top  of  each  rectangle  as  shown. 

3.  A  tabular  record  of  drawings  is  usually  made  for  each  contract. 
This  provides  for  the  initials  of  the  draftsman  and  the  checker  for  each 
drawing  with  dates  showing  when  the  drawing  is  completed  and  checked. 
Dates  are  recorded  to  show  when  prints  are  sent  for  approval  and  when 
approved,  and  when  prints  are  issued  to  the  different  shops,  to  the 
inspector,  to  the  erector,  and  to  others  interested.     These  tabular  records 
are  arranged  to  give  the  necessary  information  regarding  sheets,  but  they 
do  not  give   complete  information   regarding  the  members.     In  office- 
building  work  especially  there  are  so  many  similar  drawings,  such  as 
columns  and  beams,  that  it  is  difficult  to  make  sure  that  the  drawings 
are  prepared  in  a  logical  order  unless  supplementary  records  are  kept. 
On  account  of  limited  storage  facilities  near  the  site  of  an  ordinary 
office  building  all  material  must  be  shipped  as  required.     The  squad 
foreman  should  guard   against  having  the  roof  beams  and   columns 
detailed  while  some  on  the  first  tier  remain  untouched.     Blueprints  of 
the  plans  and  the  column  schedule  may  be  used  to  excellent  advantage 
as  progress  record  sheets,  as  explained  in  the  following  paragraphs. 

4.  Progress  Record  for  Beam  Drawings.  —  A  blueprint  of  one  of  the 
floor  plans  is  assigned  to  a  draftsman  who  is  to  prepare  the  working 
drawings  of  the  beams.     As  the  drawing  for  each  beam  is  completed, 
the  draftsman  should  mark  the  plan  with  a  distinctive  color,  say  yellow. 
An  ordinary  check  mark  is  not  sufficient  to  clearly  show  his  progress. 


160 


PART  II  — STRUCTURAL  DRAFTING 


Top  of 
C.  1.  Bases 


lnd:'cates-i-"Cap  Plats 


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PARTIAL  COLUMN  SCHEDULE 
TYPICAL  OFFICE  BUILDING 


Fig.  160.   Partial  Column  Schedule  for  an  Office  Building. 


CHAPTER  XXV 


ERECTION  PLANS  AND  DIAGRAMS 


161 


He  should  draw  the  crayon  the  full  length  of  the  beam  so  as  to  completely 
obscure  the  white  line  on  the  blueprint.  In  this  way  the  whole  tone  of 
the  print  is  changed  from  white  to  yellow,  and  the  squad  foreman  or  the 
chief  draftsman  can  tell  at  a  glance  without  interrupting  the  draftsman 
what  proportion  of  the  beams  are  detailed.  Furthermore,  when  the 
draftsman -has  completed  the  drawings  he  can  scan  the  print  and  easily 
detect  any  beam  which  he  may  have  overlooked  because  a  lone  heavy 
white  line  will  stand  out  conspicuously  among  the  yellow  lines  and  the 
fine  white  dimension  lines.  It  is  desirable  to  have  all  beams  on  one 
plan  detailed  by  one  man  in  order  to  insure  uniformity  of  details  and 
to  avoid  duplication.  If  the  available  time  will  not  permit  this,  the 
work  may  be  assigned  to  more  than  one  draftsman,  but  the  division 
should  be  made  definite  so  that  no  beam  in  one  portion  is  like  any  beam 
in  the  other  portion.  This  may  often  be  accomplished  by  assigning  the 
wall  beams  to  one  man  and  the  intermediate  beams  to  the  other.  If  a 
plan  represents  one  or  more  floors,  the  beams  for  all  the  floors  are  usually 
drawn  at  the  same  time.  Many  of  the  beams  may  be  combined  upon 
the  same  sketch  provided  different  marks  are  assigned  the  beams  of 
different  floors  as  in  C  17,  D  17,  etc.,  Fig.  92.  Another  blueprint  of 
each  plan  is  given  to  the  checker  who  marks  the  beams  as  he  checks  the 
corresponding  drawings.  He  uses  a  different  color  of  crayon,  say  red, 
but  he  marks  the  plan  in  the  same  manner  as  the  draftsman  in  order 
to  obscure  the  white  lines  of  the  beams. 

1.  A  print  of  the  column  schedule  may  be  used  for  a  progress  record 
for  the  columns.  All  records  for  one  contract  should  be  made  upon  the 
same  print.  This  may  be  posted  upon  the  wall  if  accessible  space  is 
available  or  it  may  be  filed  near  the  squad  foreman's  desk.  It  is  con- 
venient to  have  this  record  near  the  tabular  record  of  drawings,  for  the 


two  are  frequently  used  together.  Almost  any  amount  of  information 
can  be  recorded  upon  the  print  of  the  column  schedule  to  satisfy  the 
requirements  of  the  men  in  charge  of  different  drafting  rooms.  Sig- 
nificant colors  and  arrangements  may  be  used  for  different  needs.  Yel- 
low and  red  are  most  distinctive  while  green,  brown,  or  black  may  be 
used  when  additional  colors  are  desired.  The  following  suggestions 
may  be  used  as  a  guide.  Each  column  section  is  represented  by  a  rec- 
tangle bounded  by  adjacent  vertical  lines  and  heavy  horizontal  lines 
(see  above) .  Any  system  of  marks  should  be  confined  to  one  of  these 
rectangles,  the  other  rectangles  being  marked  similarly.  The  draftsmen 
should  use  the  same  color  of  crayon  (yellow)  as  in  beam  work.  In  order 
to  indicate  that  he  is  working  upon  a  certain  column  or  group  of  columns 
a  draftsman  should  draw  a  diagonal  line  across  the  rectangle  of  each 
column  of  the  group  so  that  no  one  else  will  duplicate  his  work  (see 
column  AB  31,  Fig.  160).  When  he  has  completed  the  drawing  and  it 
is  ready  to  be  checked  he  draws  the  other  diagonal  (AB  32).  The 
checker  adds  a  red  circle  or  oval  to  each  column  as  soon  as  it  is  completely 
checked  (AB33).  A  green  vertical  line  may  be  drawn  through  the 
center  of  the  rectangle  when  prints  have  been  sent  for  approval  (A  B  34) 
and  a  horizontal  brown  or  black  line  may  be  drawn  across  the  center  of 
the  rectangle  when  prints  have  been  issued  to  the  shop  (AB  35).  Other 
records  may  be  made  by  means  of  horizontal  lines  drawn  across  the 
rectangle  above  or  below  the  center,  using  any  of  the  above  colors  pro- 
vided all  horizontal  lines  with  different  significance  are  of  different 
colors.  By  drawing  the  lines  entirely  across  each  rectangle  continuous 
lines  are  formed  when  all  the  columns  are  marked.  This  simplifies  the 
detection  of  any  omissions  because  a  break  in  a  continuous  line  is 
conspicuous. 


CHAPTER  XXVI 
MATERIAL   ORDER  BILLS 

SYNOPSIS:  Preliminary  lists  of  material  are  usually  prepared  in  the  drafting  room  for 
each  contract  before  the  drawings  are  made.  These  order  bills  are  sent  to  the  Order 
Department  where  the  material  is  ordered  from  the  rolling  mills. 


1.  Purpose.  —  The  chief  function  of  a  structural  steel  company  is 
to  build  structures  from  steel  which  is  already  rolled  into  common  com- 
mercial shapes.     The  drawings  show  how  such  shapes  are  cut,  punched, 
and  combined  to  make  members  which  are  subsequently  connected  to 
form  complete  structures.     Some  companies  have  their  own  rolling  mills 
but  most  companies  procure  their  steel  shapes  elsewhere.     In  either 
case  the  material  must  be  ordered  from  the  rolling  mills.     Usually  it 
takes  so  long  to  have  an  order  filled  that  it  is  impractical  to  wait  until 
the  working  drawings  are  made  before  placing  the  order;    often  both 
the  drawings  and  the  templets  can  be  made  during  the  interval  that 
elapses  between  the  placing  of  the  mill  order  and  the  delivery  of  the 
material.     It  is  therefore  imperative  that  all  important  material   be 
ordered  as  soon  as  possible  after  a  contract  is  made. 

2.  The  original  lists  of  material  are  prepared  in  the  drafting  room  by 
men  who  are  familiar  not  only  with  drafting  room  methods  but  also  with 
the  requirements  of  the  Order  Department.     On  these  lists  the  material 
is  classified  according  to  types  of  members,  as  for  example,  columns, 
trusses,  beams,  etc.     In  the  Order  Department  new  lists  are  prepared  to 
meet  the  requirements  of  the  rolling  mills.     On  these  lists  the  material 
is  summarized  and  reclassified  according  to  sections  and  lengths  and  an 
item  member  is  assigned  to  each  different  item.     Short  plates  and  angles 
are  usually  ordered  in  multiple  lengths  to  be  cut  to  the  desired  lengths 
after  they  are  received.     Most  companies  carry  a  certain  amount  of 
material  in  stock  for  immediate  use.     The  stock  yard  is  under  the 


162 


jurisdiction  of  the  Order  Department,  where  the  necessary  material 
ordered  to  keep  the  yard  supplied  with  the  desired  amount  of  stock. 
All  additions  and  subtractions  should  be  so  recorded  that  one  can  tell 
at  any  time  just  what  material  is  in  stock.     In  the  Order  Department  i 
is  determined  whether  an  item  shall  be  taken  from  stock  or  ordered  fron  i 
the  mills. 

3.  Methods.  —  When  market  conditions  are  such  that  there  is  likel. 
to  be  considerable  delay  in  filling  an  order  it  is  especially  urgent  that  al 
main  material  be  ordered  at  once.  Capable  men  are  assigned  to  thi 
work  in  order  that  it  may  be  done  as  efficiently  and  expeditiously  a 
possible.  These  men  can  often  foresee  the  details  of  construction  wit 
sufficient  accuracy  to  enable  them  to  order  much  of  the  material  b 
referring  to  the  design  sheets.  In  more  complex  work  they  may  hav 
to  lay  out  some  of  the  details  which  determine  the  lengths  of  mai 
material.  The  lengths  of  angles  of  light  trusses  may  often  be  dete; 
mined  with  sufficient  accuracy  for  ordering  by  scaling  a  drawing  withoi 
stopping  to  calculate  the  lengths.  For  this  purpose  a  draftsman  begir 
a  working  drawing;  he  lays  down  the  working  lines  to  scale  and  drav 
the  outlines  of  the  angles.  The  angles  are  usually  ordered  about  1^ 
longer  than  the  scaled  lengths,  to  provide  for  inaccuracies.  After  tl 
lengths  are  'scaled  the  drawing  may  be  laid  aside  until  later,  if  desire' 
The  beams  and  columns  of  office  buildings  can  be  ordered  more  sati 
factorily  after  the  erection  plans  and  the  column  schedules  have  be< 
prepared,  as  explained  in  the  preceding  chapter. 


CHAPTER  XXVI 


MATERIAL  ORDER  BILLS 


163 


1.  Miscellaneous  material  other  than  structural  steel  shapes  should 
also  be  ordered  as  early  as  possible  so  that  all  will  be  available  when 
needed.     Some  of  the  more  common  examples  of  such  materials  are: 
eye  bars,  rails  and  rail  fittings,  pins,  forgings,  castings,  pipe,  corrugated 
steel  and  other  roof  and  side  coverings,  lumber,  windows  and  doors,  and 
hardware. 

2.  The  material  order  bills  are  divided  into  two  parts.     The  first  part 
is  the  main  list  of  material  and  the  corresponding  description  which  are 
made  in  the  drafting  room  in  accordance  with  this  chapter.     The  original 
sheets  are  written  with  copying  pencils;   these  originals  are  sent  to  the 
Order  Department.     A  carbon  copy  is  also  made  for  use  in  the  drafting 
room.     After  the  corresponding  mill  orders  are  written  in  the  Order 
Department,   the  second   or  central  part  of  the  original  bills  under 
"Mill  Order"  (Fig.  163),  is  filled  in  by  the  Order  Department;  copies  of 
the  sheets  are  then  made  in  a  copying  press,  and  the  originals  are  re- 
turned  to  the  drafting   room.     The  central   portion   shows  the  item 
numbers  and  other  information  required  by  the  men  who  itemize  the 
shop  bills  (page  169  :  1).     Nothing  but  the  item  number  is  given  unless 
the  number  of  pieces,  the  section,  or  the  length  differ  from  those  shown 
in  the  main  part  of  the  bill;   all  the  differences  are  recorded.     The  sec- 
tion seldom  differs  except  for  material  to  be  planed  or  recut  at  the  shop. 
The  length  may  differ  by  a  small  amount  recorded  in  the  column  headed 
"  +  ins.,"  or  by  a  large  amount  when  material  .is  in  multiple  lengths. 
The  number  of  pieces  may  differ  when  pieces  are  ordered  in  multiples 
(item  31,  Fig.  163),  or  when  similar  items  are  combined  (item  1).     In 
the  latter  case,  the  number  of  pieces  and  the  length  are  recorded  oppo- 
site the  first  item,  the  others  being  referred  to  this  by  the  words  "see 
above,"  or  "see  page —   -";  the  item  number  is  repeated. 

3.  Each  draftsman  must  make  his  drawings  conform  to  the  material 
ordered,  and  he  must  report  any  instance  where  this  is  not  feasible. 
Slight  variations  are  of  less  consequence  when  the  material  is  taken 
from  stock  or  cut  from  the  multiple  lengths  than  when  the  material 
s   cut  to  the  desired  lengths  at  the  mill.      The  draftsman  should, 
;herefore,  consult  the  original  bills  after  they  are  returned;    the  car- 
>on  copies  are  used  only  while  the  originals  are  held  by  the  Order 
Department. 


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4.   The  arrangement  and  the  description  of  the  pieces  billed  should  be 
such  that  the  material  for  any  members  may  be  easily  found  and  identi- 


164 


PART   II  —  STRUCTURAL  DRAFTING 


fied.  The  material  for  similar  members  should  be  listed  together  under 
a  separate  heading,  as  the  columns  or  the  beams  of  Fig.  163.  A  more 
detailed  description  should  be  given  opposite  each  item  of  the  bill  when- 
ever this  will  simplify  identification.  In  some  cases  the  shipping  mark, 
if  known,  can  be  used  to  advantage;  in  other  cases  it  may  be  better  to 
note  the  position  of  the  pieces  as  "Flange,"  "Stiffeners,"  "Base," 
"Crane  Seat,"  etc.  In  each  group  the  material  for  the  main  section 
should  be  listed  first,  followed  by  the  less  important  pieces.  These 
should  be  listed  in  a  systematic  order  to  facilitate  locating  them  later. 
As  a  rule  the  detailed  material  for  the  end  connections  should  be  listed 
before  that  for  the  intermediate  connections;  if  the  position  of  a  member 
on  the  drawing  can  be  anticipated,  the  material  at  the  bottom  end  or 
the  left  hand  end  should  be  billed  first. 

1.  Shipments.  —  When  contracts  are  divided  into  different  sections 
and  members  are  to  be  shipped  accordingly,  the  order  bills  should  be 
marked   "First  Shipment,"   or  similarly,  and  all  material  should  be 
grouped  under  the  proper  shipment.     The  last  page  of  bills  for  each 
shipment  should  be  marked  "Complete."     Each  tier  of  office-building 
columns  and  the  corresponding  beams  and  girders  should  be  kept  separ- 
ate from  the  others. 

2.  The  pages  of  material  order  bills  should  be  numbered  consecutively 
from  1  up.     It  may  be  preferable  to  number  the  pages  for  different  ship- 
ments in  different  series,  as  101,  102,  etc.,  for  first  shipment  and  201,  202, 
etc.,  for  the  second. 

3.  On  the  first  page  or  on  a  separate  sheet  should  be  given  information 
regarding  the  specifications,  the  grade  of  steel,  the  nature  of  any  tests 
which  are  to  be  made,  the  kind  of  oil  or  paint  to  be  applied  at  the  mill, 
and  the  name  of  the  inspector. 

4.  All  material  which  is  to  be  shipped  direct  to  the  site  should  be 
clearly  noted.    Such  material  as  corrugated  steel,  lumber,  etc.,  need  not, 
as  a  rule,  be  sent  to  the  structural  plant. 

5.  All  changes  in  material  orders  should  be  sent  to  the  order  depart- 
ment on  "change  slips,"  or  "change  orders."     These  should  coverall 
changes  or  cancellations  in  the  original  orders  whether  due  to  errors  or 
to  changes  in  design.     Such  changes  should  be  reported  at  once  so  that 
if  possible  they  may  be  made  at  the  mill  before  the  material  is  cut. 


Change  orders  should  be  made  out  for  any  material  which  is  left  over 
after  the  itemizing  is  complete  (page  169  :  1).  In  this  way  extra  material 
may  be  released,  and  made  available  for  other  contracts. 

6".  Ordered  lengths.  —  The  main  part  of  the  order  bill  should  show 
the  material  as  it  will  appear  on  the  drawings.  Any  increase  in  length 
which  is  required  on  account  of  milling,  recutting,  or  bending  at  the  shop, 
should  be  indicated  in  the  column  headed  "  +  ins."  The  lengths  which 
are  actually  ordered  from  the  mill  should  be  in  multiples  of  |  inch  wherever 
possible.  Many  of  the  shorter  pieces,  particularly  plates  and  angles,  are 
ordered  in  multiple  lengths.  The  steel  shapes  are  cut  at  the  mill  as  they 
come  from  the  rolls  still  hot.  It  is  not  practicable  to  measure  the  lengths 
with  great  precision  and  a  "mill  variation  "  in  length  is  allowed.  Hence 
it  is  inconsistent  to  order  material  in  sixteenths  or  eighths.  Some  of  the 
more  important  points  to  be  considered  in  ordering  material  will  now  be 
taken  up  for  the  different  shapes. 

7.  Beams.  —  Because  of  the  difficulty  and  the  waste  incident  to 
cutting,  I-beams  and  channels  are  usually  ordered  so  that  they  can  be 
used  as  they  are  received  from  the  mills,  unless  they  are  to  be  milled 
(page  31  :  1).  The  standard  mill  variation  in  length  for  overrun  or 
underrun  is  f  inch.  Greater  allowance  is  made  if  feasible  so  that  a  beam 
need  not  be  recut  in  the  shop  even  though  it  overruns  more  than  f  inch 
(see  page  88  :  1).  Beams  which  frame  between  other  beams  are  usually 
ordered  about  1J  inches  less  than  the  distance  between  the  centers  of  the 
webs  of  the  supporting  I-beams  or  channels.  Beams  which  frame  be- 
tween girders  or  columns  are  usually  ordered  about  1  inch  less  than  the 
dear  distance  between  the  supports.  Runway  beams  which  support  the 
wheels  directly  should  be  milled  to  give  about  f-inch  clearance  between 
the  ends  of  adjacent  beams.  I-beams  and  channels  which  form  parts  of 
columns  or  chord  members  are  often  milled  on  the  ends  after  they  are 
assembled  in  order  to  give  uniform  bearing.  Beams  to  be  milled  should 
be  ordered  long  enough  to  permit  recutting.  If  milled  at  one  end  %  inch 
is  added;  if  milled  at  both  ends  J  inch  is  added.  This  increase  is  indi- 
cated in  the  column  headed  "-(-  ins.,"  and  the  order  department  takes 
this  into  account  in  preparing  the  mill  order.  Beams  used  as  purlins 
are  usually  ordered  about  1  inch  less  than  the  distance  center  to  center  of 
trusses,  the  length  being  taken  to  the  nearest  5  inch.  This  applies  alsc 


CHAPTER  XXVI 


MATERIAL  ORDER  BILLS 


165 


to  angle,  tee,  or  Z-bar  purlins.  I-beams  and  channels  which  are  to  be 
sawed  diagonally  at  the  shop  should  be  ordered  about  1  inch  long.  Short 
I-beams  so  cut  may  be  ordered  in  multiple  lengths  to  save  waste  (compare 
Fig.  44),  allowing  about  \  inch  waste  for  each  saw  cut. 

1.  Angles  can  be  recut  at  the  shop  more  easily  than  beams,  hence  it  is 
not  so  important  to  use  the  exact  lengths  that  come  from  the  mill.     The 
angles  are  not  likely  to  underrun  the  ordered  lengths  but  they  may  over- 
run as  much  as  f  inch.     Better  results  are  obtained  when  the  angles  are 
sheared  to  the  proper  lengths  at  the  shop.     The  main  flange  or  chord 
angles  of  girders,  columns,  trusses,  etc.,  are  usually  ordered  about  f  inch 
long  to  make  recutting  necessary  whether  or  not  these  angles  are  to  be 
milled.     Angles  which  are  to  be  milled  at  one  end  only  are  ordered  J  inch 
long.     These  increases  are  indicated  in  the  column  headed  "ins."     Stiff- 
ening angles  need  not  be  ordered  long  unless  they  exceed  |  inch  in  thick- 
ness when  they  must  be  milled,  or  unless  they  are  crimped.     Two  or  more 
angles  of  the  same  length  may  be  cut  from  one  piece,  provided  the  sum 
does  not  exceed  one  car-load  length  of  30  or  35  feet.     All  angles  less  than 
3  feet  long  are  ordered  in  multiple  lengths;  angles  more  than  3  feet  long 
are  seldom  combined  unless  they  are  of  the  same  length  or  so  nearly  the 
same  that  the  length  of  the  longest  may  be  used  for  each.     When  more 
than  two  pieces  are  ordered  in  multiple,  the  length  should  be  increased 
to  allow  for  waste;    j  inch  should  be  added  for  each  cut,  and  usually 
enough  more  to  bring   the   total  to  an  even  inch.      Crimped   angles 
must  be  increased  in  length  by  the  depth  of  each  crimp  (page  97 : 1)  and 
also  by  \  inch  for  each  crimp  to  provide  for  recutting  after  crimping. 
Angle  purlins  are  ordered  about  1  inch  less  than  the  distance  center  to 
center  of  trusses,  the  length  being  taken  to  the  nearest  J  inch.     Bent 
angles  should  be  ordered  about  3  inches  long;    curved  angles  should 
be  ordered  about  6  inches  long. 

2.  Plates.  —  In  this  book  no  distinction  in  terminology  has  been  made 
between  plates  of  different  sizes  and  forms.     In  ordering  material  from 
the  mill,  however,  more  specific  terms  must  be  used,  according  to  the 
aandbook  of  the  steel  company  from  which  the  material  is  ordered. 
'Flats  "  and  "Universal  Mill  "  or  "edged  "  plates  are  rolled  between 
/ertical  rolls  as  well  as  between  horizontal  rolls;  these  plates  have  rolled 
:dges  as  distinguished  from  "sheared  plates  "  which  are  rolled  between 


horizontal  rolls  only,  and  then  sheared  to  the  desired  widths.  Flats 
include  all  widths  up  to  6  or  7  inches,  Universal  Mill  (U.  M.)  plates  from 
7  or  8  inches  up  to  36  or  48  inches,  and  sheared  plates  from  24  inches  up 
to  126  or  132  inches.  Plates  may  be  sheared  less  than  24  inches  if  de- 
sired. Up  to  48  inches  either  U.  M.  or  sheared  plates  will  be  furnished 
at  the  option  of  the  manufacturers  unless  one  or  the  other  is  specified. 
Flats  are  rolled  in  widths  which  are  multiples  of  \  inch  with  a  mill  varia- 
tion of  g  inch.  Widths  less  than  3  inches  are  rolled  in  multiples  of  j  inch. 
U.  M.  plates  are  regularly  rolled  only  in  widths  which  are  multiples  of 
1  inch,  with  a  mill  variation  of  |  inch.  Sheared  plates  may  be  ordered 
in  widths  which  are  multiples  of  \  inch  with  a  mill  variation  of  \  inch; 
preferably  these  plates  should  be  ordered  in  multiples  of  1  inch.  Some 
widths  are  used  more  commonly  than  others,  and  except  on  large  orders 
it  is  better  to  use  these  common  sizes  as  far  as  practicable.  Each  com- 
pany should  provide  its  designers  and  draftsmen  with  a  list  of  preferred 
sizes  including  the  sizes  carried  in  stock.  The  extreme  lengths  of  plates 
vary  with  the  cross  sections.*  The  lengths  of  U.  M.  plates  are  not 
likely  to  underrun  the  ordered  lengths  but  they  may  overrun  f  inch. 
Sheared  plates  may  underrun  \  inch  or  overrun  \  inch.  Flats  over 
20  feet  long  may  underrun  lj  inches  or  overrun  f  inch;  shorter  flats 
will  vary  only  about  one  half  these  values.  Plates  are  usually  recut  at 
the  shop  except  in  special  cases;  for  example,  the  webs  and  the  cover 
plates  of  girders  are  often  used  as  delivered.  Such  webs  should  be 
ordered  from  \  to  J  inch  less  than  the  extreme  lengths  back  to  back 
of  end  angles,  or  if  spliced,  \  to  \  inch  less  than  the  distances  between 
the  centers  of  splices.  No  individual  portion  of  a  web  should  weigh 
more  than  3000  pounds.  Full-length  cover  plates  are  usually  ordered 
about  f  inch  long  for  recutting ;  others  need  not  be  recut  provided 
the  rivets  are  spaced  to  allow  for  variation  (page  106  :  2) .  Cover  plates 
are  usually  specified  U.  M.,  particularly  if  exposed  to  the  elements, 
for  the  rolled  edges  do  not  corrode  so  quickly.  Some  of  the  heavier 
gusset  plates  are  ordered  as  "sketch  plates,"  i.e.,  they  are  cut  to  irregular 
shapes  at  the  mill  according  to  dimensioned  sketches.  There  is  an  extra 
charge  for  this  work  which  will  usually  offset  any  saving  in  material 

*  See  the  handbooks  of  the  different  steel  manufacturers,  or  Ketchum's  "Structural 
Engineers'  Handbook,"  McGraw-Hill  Book  Company,  Inc.,  New  York. 


166 


PART   II  —  STRUCTURAL   DRAFTING 


unless  the  plates  are  over  3  feet  long  and  f  inch  thick.  Sketch  plates 
should  only  be  ordered  upon  the  approval  of  an  experienced  man.  Gus- 
set plates  may  often  be  cut  from  multiple  lengths  with  little  or  no  waste, 
provided  the  diagonal  cuts  extend  entirely  across  the  plate,  as  in  Fig. 
44.  Advantage  should  be  taken  of  this  fact  in  ordering  the  material. 
Multiple  lengths  should  not  be  ordered  too  closely;  it  is  better  to  allow 
j  inch  extra  for  each  cut  and  to  increase  the  total  length  to  an  even  inch. 
Plates  which  are  to  be  planed  should  have  due  allowance  made  for  waste. 
The  widths  should  be  increased  $  inch  for  each  edge  planed;  the  thick- 
nesses should  be  increased  ^  inch  for  each  side  planed;  for  plates  over 
3  feet  square  the  latter  should  be  increased  according  to  plant  standards. 
1.  Lattice  bars,  short  tie  or  sag  rods,  gas  pipe  and  some  other  mis- 


cellaneous pieces  are  usually  ordered  according  to  the  approximate  total 
number  of  linear  feet  (Fig.  163);  these  lengths  can  be  converted  to  mul- 
tiple lengths  by  the  Order  Department. 

2.  Rails  for  crane  runways,  etc.,  should  be  ordered  according  to 
standard  lengths.  Odd  lengths  may  be  ordered  for  one  end  of  a  runway 
to  provide  the  proper  total  length.  Rails  which  weigh  over  60  pounds 
per  yard  are  usually  furnished  in  33  foot  lengths;  lighter  sections  come  in 
30  foot  lengths.  Specify  "standard  punching  in  ends"  if  such  spacing 
(page  317)  is  required;  this  punching  is  done  at  the  mill.  All  special 
punching  must  be  done  at  the  shop.  If  there  is  no  special  punching  or 
cutting  the  rails  can  usually  be  shipped  directly  from  the  mill  to  the  site; 
if  this  is  desired  it  should  be  so  noted  on  the  order  bills. 


CHAPTER  XXVII 


SHOP  BILLS  AND   SHIPPING  BILLS 

SYNOPSIS:  Lists  of  the  component  parts  of  all  members  of  a  structure  are  summar- 
ized on  shop  bills  for  use  in  gathering  the  proper  material  together.  The  completed 
members  are  listed  on  shipping  bills  for  the  use  of  the  shipper. 


1.  A  shop  bill  is  a  detailed  list  of  all  the  material  of  which  one  or  more 
members  are  composed.     Shop  bills  are  made  for  all  material  (except 
shop  rivets),  which  is  fabricated  in  the  shop  in  accordance  with  the  draw- 
ings.    They  do  not  include  lumber,  corrugated  steel,  hardware,  or  other 
materials  which  are  shipped  without  shop  work  directly  from  the  manu- 
facturers to  the  site.     Shop  bills  are  used  primarily  by  men  in  the  receiv- 
ing yard  or  stock  yard;   these  men  select  the  material  for  each  member 
and  deliver  it  to  the  structural  shop  as  needed.     Much  of  this  material  is 
used  as  it  comes  from  the  rolling  mill  but  some  must  be  recut  to  shorter 
lengths  according  to  information  given  on  the  shop  bills.     Incidentally, 
shop  bills  are  used  as  check  lists  in  different  shops;   thus  for  example,  in 
the  templet  shop  each  item  is  checked  off  on  the  shop  bill  as  soon  as  the 
corresponding  templet  is  completed. 

2.  Form.  —  Shop  bills  may  be  made  on  separate  sheets,  or  they  may 
be  combined  with  shipping  bills  (page  171  :  1),  or  with  drawings  and 

hipping  bills  (page  174  :  1).  When  made  on  separate  sheets  no  shop  bill 
should  contain  the  material  for  more  than  one  sheet  of  drawings.  This 
s  to  simplify  the  distribution  of  the  proper  shop  bills  with  each  drawing; 
n  fact,  they  are  sometimes  attached  to  the  drawing.  These  shop  bills 
should  be  numbered  to  correspond  to  the  drawing  number;  thus  the  shop 
jill  for  drawing  number  3  is  marked  S  3,  and  for  drawing  number  6  it  is 
narked  S  6.  If  more  than  one  page  of  shop  bills  are  required  for  a  single 
sheet  of  drawings,  they  should  be  numbered  a,  b,  c,  etc.,  thus:  —  S  4a, 
3  46,  S  4c,  are  all  for  the  drawings  on  sheet  number  4.  Combination 


bills  are  numbered  consecutively,  as  explained  on  page  54:5.  Shop  bills 
should  be  made  with  freehand  letters,  usually  directly  in  ink  without 
preliminary  penciling.  According  to  common  drafting-room  parlance, 
they  are  said  to  be  "written  "  but  this  should  not  be  interpreted  to  imply 
the  use  of  script.  Above  all,  the  figures  should  be  carefully  made. 

3.  A  shop  bill  is  divided  into  three  parts.     The  first  part  is  the  sum- 
mary of  material  taken  from  the  drawing;   this  part  is  confined  to  the 
left  half  of  the  shop-bill  form,  including  the  "Remarks"  (Fig.  168). 
This  part  of  the  shop  bill  is  usually  written  by  boys  or  young  men  who 
are  beginning  their  careers  in  the  drafting  room.     For  efficiency  these 
billers  often  work  in  a  separate  squad  in  charge  of  a  Chief  Biller.     A  bill 
may  be  checked  by  another  member  of  the  squad,  but  more  satisfactory 
results  are  usually  obtained  if  each  shop  bill  is  checked  by  the  draftsman 
who  made  the  corresponding  drawing;   this  is  especially  desirable  if  the 
drawing  is  complex.     The  signatures  at  the  bottom  of  the  shop  bill  are 
for  the  men  who  make  and  check  this  first  part.     The  second  part  of  a 
shop  bill  is  the  itemizing,  as  explained  on  page  169  :  1.     These  two  parts 
must  be  completed  before  the  bills  are  printed  for  the  shop.     The  third 
part  is  the  calculation  of  the  weights  of  members,  as  explained  on  page 
170  :  1.     The  weights  are  not  usually  computed  unless  the  contract  is 
let  on  a  pound  price  basis. 

4.  Arrangement.  —  In  the  first  part  of  a  shop  bill  should  be  listed  all 
the  material  required  in  making  all  the  members  which  are  detailed  to- 
gether, whether  or  not  the  members  bear  the  same  mark.     Thus,  in  Fig. 


167 


168 


PART  II  —  STRUCTURAL  DRAFTING 


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Fig.  168.   Typical  Shop  Bills. 


CHAPTER  XXVII 


SHOP  BILLS  AND  SHIPPING  BILLS 


109 


168  is  included  all  the  material  required  in  making  the  two  chord  members 
of  Fig.  124.  When  only  part  of  a  member  is  shown  on  the  drawing  all 
notes  which  affect  the  bill  of  material  must  be  carefully  considered. 
Thus  for  a  member  marked  "Symmetrical  about  the  center  line  "  much  of 
the  material  billed  on  the  drawing  should  be  doubled.  When  more  than 
one  drawing  is  made  on  a  sheet  the  members  should  be  grouped  on  the 
shop  bill  in  the  same  way  they  are  grouped  on  the  drawing,  as  illustrated 
in  Fig.  168,  which  shows  the  shop  bill  for  the  girts  and  struts  of  Fig.  147. 
One  or  more  blank  lines  should  be  left  to  separate  the  groups  and  to 
provide  a  space  for  the  total  weight  where  necessary  (page  170  : 1).  The 
number,  the  name,  and  the  mark  of  each  different  member  should  be 
printed  prominently  at  the  head  of  each  group  without  regard  to  the 
vertical  lines.  Usually  only  one  mark  is  put  on  a  line,  as  F  7  and  F  8,  or 
8  4,  S  5  and  .S  6  (Fig.  168),  although  two  may  sometimes  be  combined 
as  F  9K  and  F  QL,  if  it  is  desired  to  save  space.  Members  which  are  com- 
posed of  single  pieces  may  be  billed  on  a  single  line,  as  F  10  or  M  5 
(compare  page  173  :  1).  Fine  vertical  lines  are  printed  under  "sections  " 
as  an  aid  to  uniformity  in  billing.  With  these  lines  it  is  unnecessary  to 
use  crosses.  All  four  columns  are  used  for  angles  but  the  second  one  need 
not  be  used  for  plates.  For  beams  the  sign  (#)  may  be  placed  in  the  last 
column.  The  material  should  be  listed  systematically,  beginning  with 
the  main  material.  The  details  should  be  grouped  as  on  the  drawing, 
beginning  at  the  bottom  or  left  hand  end  of  a  member  and  proceeding 
toward  the  other  end.  The  washers  and  bolts  for  any  member  should  be 
the  last  items  to  be  billed.  Each  item  which  is  not  common  to  all  the 
members  of  a  group  should  be  so  noted,  as  in  Fig.  168.  Similarly,  notes 
should  appear  opposite  each  item  which  is  "Milled"  or  "Finished" 
(abbreviated  "Fin"),  "Bolted  complete,"  or  "Bolted  for  Shipment." 
Assembling  marks  should  be  recorded  in  a  special  column  headed  "Piece 
Mark."  Permanent  bolts  are  usually  listed  on  the  drawing,  hence  they 
are  billed  as  a  matter  of  course.  Temporary  bolts  used  to  hold  loose 
pieces  in  position  during  shipment  are  usually  of  odd  lengths  picked  up 
in  the  shop;  these  are  not  always  listed  on  the  shop  bill,  but  they  should 
be  so  listed  for  a  "pound  price  "  contract.  It  is  usually  sufficient  to  bill 
all  temporary  bolts  as  3  inches  long;  in  this  way  an  average  weight  is 
provided  for  without  undue  investigation  of  details  which  would  be 


inconsistent  with  the  usual  shop  practice.  The  column  headed  "  +  ins." 
is  used  only  when  the  material  is  ordered  directly  from  the  shop  bills 
instead  of  from  preliminary  order  bills,  as  for  example,  when  shop  bills  are 
written  for  drawings  made  by  a  consulting  engineer.  In  this  case  the 
complete  shop  bills  can  be  prepared  as  quickly  as  preliminary  bills;  the 
latter  may  be  dispensed  with  and  much  duplication  may  be  thus  avoided. 
The  use  of  this  column  on  the  shop  bill  is  then  the  same  as  on  the  material 
order  bill  (page  164  :  6). 

1.  Itemizing.  — The  second  part  of  the  shop  bill  shows  the  ordered 
material  from  which  the  yard  men  should  select  the  steel  for  the  different 
component  parts  of  a  member.  All  material  which  is  ordered  specially 
for  a  contract  has  the  contract  number  and  an  item  number  painted  on 
the  steel.  This  item  number  appears  on  the  preliminary  material  order 
bill  (page  163  :  2)  and  it  is  transferred  to  the  shop  bill  to  indicate  the 
proper  assignment  of  material.  The  term  "Itemizing"  is  applied  to 
the  preparation  of  this  part  of  the  shop  bill.  The  best  results  are  ob- 
tained if  one  man  itemizes  all  of  the  shop  bills  of  a  single  contract,  or 
at  least  of  a  definite  portion  of  it;  this  man  should  be  conversant  with 
the  practice  of  the  Order  Department.  Opposite  each  component  part 
of  a  member  should  be  placed  the  item  number  of  the  material  from 
which  ;t  is  taken,  and  suitable  notation  should  be  made  on  the  material 
order  bill  so  that  the  same  pieces  will  not  be  used  again.  The  other 
columns  under  "Mill  Order  "  are  not  necessarily  used  in  all  cases.  In 
general  the  number  of  pieces  need  not  be  given  unless  the  material  is 
to  be  ordered  from  the  shop  bill  instead  of  from  a  material  order  bill, 
in  which  case  the  order  department  takes  care  of  the  whole  Mill  Order 
and  no  itemizing  is  done  in  the  drafting  room.  The  section  need  be 
entered  only  when  it  differs  from  that  listed  in  the  main  part  of  the  bill. 
For  example,  an  angle  which  is  to  be  cut  from  another  size  should  be  so 
noted  on  the  drawing,  as  IL5%X3X%X  l'-2  (cut  from  6  X  3), 
illustrated  in  the  bracket  on  D  13,  Fig.  140;  in  the  main  part  of  the 
shop  bill  it  should  be  billed  5J  X  3  X  f  and  the  original  biller  should 
record  6  X  3  X  f  in  the  corresponding  place  under  the  Mill  Order. 
The  itemizer  then  provides  for  the  6  X  3  X  f  angle.  Similarly,  plates 
may  be  cut  from  other  sizes.  Sometimes  small  plates  are  changed  so 
that  the  length  becomes  the  width,  as  for  example,  a  plate  billed  6  X 


170 


PART   II  —  STRUCTURAL   DRAFTING 


I  X  I'-O  may  be  itemized  as  a  12  X  \  X  6  plate.  Plates  which  are 
ordered  as  sketch  plates  (page  165  :  2),  should  be  noted  as  in  Fig.  168. 
The  length  need  be  given  only  when  it  differs  from  the  length  billed  in 
the  main  part  of  the  bill.  This  may  differ  by  only  a  fraction  of  an 
inch,  as  in  material  to  be  milled  (page  165  :  1),  or  by  a  large  amount 
when  ordered  in  multiple  lengths  (page  165  :  2).  On  account  of  differ- 
ent grouping  on  the  shop  bill  and  the  order  bill  the  number  of  pieces 
will  often  differ.  Sometimes  more  than  one  item  number  will  have  to 
be  placed  opposite  a  single  entry  on  the  shop  bill,  the  number  taken 
from  each  being  recorded  under  "No.  of  Pieces."  More  frequently  the 
number  of  pieces  listed  on  the  shop  bill  will  be  less  than  the  number  on 
the  order  bill;  care  should  be  taken  to  make  the  proper  record  on  the 
order  bill  so  that  the  same  pieces  will  not  be  reassigned.  Beam  sepa- 
rators or  other  materials  which  are  assembled  in  the  shop  with  the  beams 
or  other  members,  should  be  billed  with  them  in  accordance  with  the 
drawings.  When  these  materials  are  made  from  combination  bills  they 
should  be  itemized  on  the  latter;  to  save  duplication  they  should  not  be 
itemized  on  the  shop  bill  but  reference  should  be  made  to  the  combina- 
tion bill,  as  in  Fig.  172.  All  material  that  is  not  provided  for  on  the 
order  bill  should  be  itemized  by  the  order  department.  Presumably 
this  material  will  be  taken  from  the  plant  stock,  because  care  should  be 
taken  to  write  advance  orders  for  all  material  which  cannot  be  found  in 
stock.  Material  taken  from  stock  has  no  item  number,  but  it  is  indi- 
cated by  the  capital  letter  S  instead.  No  length  need  be  recorded  for 
stock  items,  but  the  section  should  be  indicated  if  it  differs  from  the 
billed  section. 

1.  When  a  contract  is  based  upon  a  certain  price  per  pound,  the 
payments  are  determined  by  the  calculated  weight.  The  scaled  weights 
are  used  as  an  approximate  check.  For  each  contract  the  method  of 
computation  should  be  agreed  upon,  but  undue  refinements  should  be 
avoided.  Usually  the  weights  are  determined  from  the  material  sum- 
marized on  the  main  part  of  the  shop  bills;  to  these  are  added  the 
weights  of  the  heads  of  the  shop  rivets.  Thus  no  deduction  is  made  for 
corners  cut  off  (except  for  plates  ordered  by  sketch),  nor  for  holes  for 
field  rivets  or  pins;  the  holes  for  shop  rivets  are  filled  by  the  rivet  shanks 
so  that  the  weight  is  not  affected.  The  weights  are  expressed  to  the 


nearest  pound;  when  members  are  composed  of  a  large  number  of  com- 
ponent parts  it  may  be  necessary  to  carry  the  partial  weights  to  one 
decimal.  The  weights  are  recorded  in  ink  on  the  shipping  bills,  each 
weight  being  for  a  single  member.  The  shipper  weighs  each  car  load 
and  compares  the  weight  with  the  sum  of  the  calculated  weights  of  the 
corresponding  members;  since  the  number  of  members  shipped  on  one 
car  seldom  equals  the  total  number  of  members  which  are  alike,  the 
weight  of  a  single  member  is  more  useful  than  the  total  weight  would 
be.  The  shop  bills  are  used  for  convenience  in  determining  the  weights 
of  members;  these  weights  are  ultimately  transferred  to  the  shipping 
bills.  The  weights  on  the  shop  bills  are  used  simply  as  a  means  toward 
this  end,  and  for  this  reason  it  is  unnecessary  to  ink  them;  in  fact  all 
necessary  prints  of  the  shop  bills  may  be  made  before  the  weights  are 
added.  Usually  the  weights  are  computed  and  checked  by  young  men 
who  specialize  in  that  work,  although  the  draftsmen  are  sometimes 
asked  to  help.  Most  companies  have  exhaustive  tables  to  facilitate 
this  work.  In  computing  the  weight  of  one  member,  the  weight  of  the 
corresponding  number  of  component  parts  should  be  found.  Thus  for 
each  girt,  F  7  or  F  8  (Fig.  168),  there  are  two  plates  and  two  belts;  the 
weights  should  be  entered  accordingly.  Usually  the  first  step  in  com- 
puting weights  is  to  determine  from  the  tables  the  weights  per  foot  for 
different  sections.  These  weights  may  be  recorded  in  the  column  pro- 
vided for  that  purpose;  the  weights  of  I-beams  and  channels  are  given 
in  the  main  part  of  the  shop  bill  so  they  need  not  be  repeated.  The 
weight  of  each  item  is  the  product  of  three  factors,  viz:  the  weight  per 
foot,  the  length  in  feet,  and  the  number  of  pieces  per  member.  The 
order  in  which  these  factors  are  multiplied  depends  upon  the  method 
used  and  upon  the  factors  themselves;  it  may  be  more  convenient  to 
multiply  the  length  by  one  of  the  other  factors  before  the  inches  and 
fractions  are  converted  to  decimals  of  a  foot.  The  weights  should  be 
placed  in  the  spaces  provided  for  them;  fine  vertical  lines  are  printed 
on  the  forms  to  simplify  the  alignment  of  figures  for  totaling.  When 
all  members  of  a  group  weigh  the  same,  a  line  can  be  drawn  under  the 
weight  of  the  last  component  part  and  a  single  total  can  be  recorded  in 
the  blank  space  between  groups,  as  for  F  9.  When  the  weights  of  thf 
members  of  a  group  differ,  each  must  have  its  own  total;  to  save  spac< 


CHAPTER  XXVII 


SHOP  BILLS  AND  SHIPPING  BILLS 


171 


each  total  may  bo  recorded  opposite  the  mark  of  the  proper  member, 
as  for  F  7  and  F  8  or  for  S  4,  S  5  and  S  6.  Care  must  be  taken  to  in- 
clude in  these  totals  only  the  weights  of  the  component  parts  which 
form  the  corresponding  members.  The  weights  of  the  rivet  heads  should 
not  be  overlooked.  Since  they  do  not  appear  on  the  shop  bill  they  must 
be  counted  from  the  drawings  and  their  weights  must  be  entered  upon 
the  shop  bill,  as  in  Fig.  168.  In  counting  shop  rivets  special  attention 
should  be  given  to  symmetrical  notes,  and  to  group  spacing;  each 
rivet  has  two  heads.  The  weights  of  rivets  and  bolts  are  given  on 
page  304.  The  weight  of  a  bolt  or  a  rivet  may  be  obtained  by  the 
proper  combination  of  the  weights  of  the  head,  the  nut,  and  the  shank 
of  proper  length.  The  weights  of  standard  connection  angles  for  beams 
include  the  weights  of  the  shop  rivet  heads. 

1.  A  shipping  bill  is  a  summary  of  members  in  the  form  in  which  they 
are  to  be  shipped.  It  is  made  primarily  as  a  check  list  for  the  shipper. 
All  members  which  bear  the  same  shipping  mark  should  be  billed  on  the 
same  line,  but  different  marks  should  be  listed  separately.  In  each 
case  the  number,  the  name,  the  mark,  and  the  shipping  dimensions 
should  be  given;  the  weight  is  given  only  when  required  (page  170  : 1). 
The  sheet  number  of  the  drawing  is  also  recorded.  A  portion  of  the 
bill  is  printed  black  so  that  white  spaces  will  be  left  on  the  blue  prints 
for  the  convenience  of  the  shipper  in  making  records  of  shipments. 
The  shipping  dimensions  are  usually  given  to  the  nearest  inch  (or  half- 
inch).  The  extreme  "box  dimensions  "  are  given,  i.e.,  the  three  dimen- 
sions of  a  box  which  would  contain  the  member.  The  length  is  given  in 
feet  and  inches  but  the  other  two  dimensions  at  right  angles  to  the 
length  and  to  each  other  are  expressed  in  inches,  the  larger  of  the  two 
being  given  first.  In  case  these  dimensions  do  not  fairly  represent  a 
large  member,  a  freehand  sketch  with  auxiliary  dimensions  may  be 
drawn  in  the  column  headed  "Remarks,"  as  shown  in  Fig.  171.  Mem- 
bers should  be  listed  preferably  in  about  the  order  in  which  they  will 
be  erected.  When  part  of  a  structure  is  to  be  completed  before  the 
i rest  is  begun,  the  material  should  be  billed  and  shipped  accordingly; 
;he  shipping  bills  should  be  marked  /with  the  shipment,  as  for  example, 
'First  Shipment."  The  last  page  for  any  shipment  should  be  marked 
'Complete."  Shipping  bills  are  numbered  consecutively,  usually  with 


UNIVERSITY   BRIDGE  COMPANY 

AMBKIDGC_  .„ 


Fig.  171.  Typical  Shipping  Bill. 

a  distinctive  letter  as  R  1,  R  2,  etc.  Bills  for  different  shipments  may 
be  numbered  in  different  series  as  R  101,  R  102,  etc.,  for  1st  shipment 
and  R  201,  R  202,  etc.,  for  2nd  shipment. 


172 


PART   II  —  STRUCTURAL   DRAFTING 


UNIVERSITY    BRIDGE    COMPANY 

YALE 

' 


BILL  P4»OE  BY . DAIE_ CONIRACI 

BILL  CHECKED  BY ^- DATE_1  „ SHEET  NUMBER 


Fig.  172.  Typical  Shop  and  Shipping  Bills. 


CHAPTER   XXVII 


SHOP   BILLS  AND   SHIPPING   BILLS 


173 


1.  Shop  and  Shipping  Bills  are  often  combined  on  the  same  form,  as 
in  Fig.  172.  This  is  done  when  the  shop  bill  for  each  member  of  a 
drawing  occupies  only  a  few  lines,  i.e.,  when  each  member  is  composed 
of  but  few  different  parts.  These  simple  shop  bills  may  be  arranged 
to  give  the  necessary  information  to  the  shipper  so  that  special  shipping 
bills  need  not  be  prepared.  It  would  not  be  feasible  to  use  combined 
forms  for  complex  members  because  the  shipping  data  would  be  obscured 
by  the  details,  and  the  shipper  would  be  burdened  with  an  unneces- 
sarily large  number  of  pages.  Usually  the  combined  shop  and  shipping 
bills  are  used  for  beam  work  and  other  simple  work  drawn  on  small 
sheets  or  printed  forms  (except  those  mentioned  in  the  following  para- 
graph) ;  they  are  sometimes  used  for  simple  members  drawn  on  large 
sheets.  For  example,  the  girts  and  struts  of  Fig.  147  might  be  billed 
on  such  a  form  instead  of  as  in  Fig.  168.  In  the  combined  form  the 
number,  the  name,  and  the  mark  are  listed  in  columns  as  in  shipping 


bills,  except  that  they  are  grouped  as  on  the  drawing.  The  remainder 
of  the  bill,  except  the  shipper's  record,  is  similar  to  the  shop  bill  form. 
The  bill  of  material  may  be  started  on  the  same  line  as  the  mark,  unless 
members  which  bear  different  marks  are  grouped  together;  in  this 
case,  it  is  better  to  begin  on  the  line  below  the  last  mark  to  avoid  the 
confusion  that  might  arise  if  part  of  the  material  were  billed  opposite  one 
of  the  marks.  Blank  lines  should  be  left  between  groups.  In  some  work 
such  as  structures  intended  for  export,  the  extreme  shipping  dimensions 
are  given  opposite  each  mark,  just  above  the  detailed  list  of  material. 
The  billed  length  of  a  beam  is  the  length  which  appears  on  the  drawing 
along  with  the  depth  and  the  weight  —  usually  the  ordered  length. 

2.  Shop  and  shipping  bills  are  sometimes  combined  with  the  drawing, 
as  illustrated  in  Fig.  175  (a)  and  (6).  The  bill  portion  of  these  combina- 
tion sheets  is  much  the  same  as  for  shop  and  shipping  bills  explained 
in  the  preceding  paragraph. 


CHAPTER  XXVIII 
MISCELLANEOUS   DRAWINGS  AND   LISTS 

SYNOPSIS  :  Some  of  the  more  simple  drawings  may  be  combined  with  the  correspond- 
ing shop  and  shipping  bills  on  the  same  sheet;  the  use  of  these  combination  sheets  is 
illustrated.  The  method  of  listing  field  rivets  and  bolts  is  explained  also. 


1.  Much  of  the  miscellaneous  material  used  in  steel  construction  is 
of  such  a  nature  that  comparatively  little  information  need  be  given  on 
the  drawings.     This  may  be  because  there  is  little  or  no  shop  work  to 
be  done,  or  because  most  of  the  shop  work  is  to  be  carried  out  according 
to  fixed  standards  which  need'not  be  duplicated  on  the  drawings.     Such 
material  is  usually  drawn  on  a  combination  sheet  of  the  general  form 
shown  in  Fig.  175  (a)  or  (6).     The  use  of  such  forms*  reduces  the 
number  of  sheets  and  saves  duplication,  because  a  working  drawing,  a 
shop  bill,  and  a  shipping  bill  are  all  contained  on  the  same  sheet.     These 
sheets  are  used  for  rods,  anchor  bolts  and  washers,  bearing  plates  and 
anchors,  rollers,  crane  stops,  castings,  forgings,  etc.     Standard  castings 
such  as  beveled  or  "O.G."  washers,  separators,  or  rail  clamps  may  be 
listed  without  a  drawing  if  reference  is  made  to  a  standard  pattern 
number.     When  beam  separators  are  to  be  assembled  in  the  shop  and 
shipped  with  beams  in  the  form  of  beam  girders,  a  note  to  that  effect 
should  be  placed  on  the  preliminary  bill  or  combination  sheet  from 
which  they  are  made  so  they  will  not  be  shipped  separately.     Reference 
to  this  sheet  should  be  made  on  the  shop  bill,  as  shown  in  Fig.  172. 
Castings  and  forgings  should  be  listed  on  separate  sheets  for  they  are 
made  in  different  departments. 

2.  Special  printed  forms  are  used  by  many  companies  to  simplify 
the  drafting.     Such  forms  are  commonly  used  for  crane  rails,  eye  bars, 
loop  rods,  pins,  clevises,  turnbuckles,  corrugated  steel,  etc.     A  general 

*  See  footnote,  page  83 


drawing  of  one  of  these  pieces  is  printed  on  each  form  with  blank  dimen- 
sions to  be  filled  in.  The  forms  may  be  so  arranged  that  the  different 
variables  may  be  recorded  in  tabular  form;  in  this  way  similar  pieces 
in  any  contract  may  be  listed  upon  the  same  sheet  conveniently. 

3.  The  use  of  a  combination  sheet  with  a  comparatively  large  space 
for  the  drawing  is  shown  in  Fig.  175  (a)  which  illustrates  a  typical  cast- 
iron  base  f   for   an   office-building   column.      The   tabular  portion   is 
arranged  as  a  combination  shop  and  shipping  bill  (page  173  :  1);  not  all 
of  the  blanks  are  required  for  castings.     Note  that  the  tops  of  these  cast 
bases  are  finished  to  furnish  uniform  bearing  for  the  columns.     Holes 
are  drilled  in  the  tops  for  the  bolts  which  hold  the  columns  in  place 
during  erection;    it  would  be  impracticable  to  punch  holes  or  to  drive 
rivets  in  cast  iron  because  of  the  danger  of  cracking  the  casting.     Cored 
holes  (cast  in  place)  are  sometimes  used  for  bolts,  but  they  should  be 
made  f  inch  larger  than  the  bolts  to  allow  for  irregularities  in  the  casting. 
Holes  are  cored  in  the  bottoms  of  large  cast  bases  to  permit  the  more 
even  distribution  of  grout  which  is  poured  after  the  bases  are  in  place. 

4.  The  use  of  a  combination  sheet  arranged  for  a  large  number  of 
items  with  comparatively  small  drawing  space  is  shown  in  Fig.  175  (&). 
This  illustrates  the  rods  for  the  mill  building  shown  in  Fig.  156.     It  is 
perhaps  necessary  to  show  more  complete  drawings  for  some  rods,  and 

t  For  a  table  of  dimensions  of  the  American  Bridge  Company's  standard  cast-iron 
bases,  see  Ketchum's  "Structural  Engineers'  Handbook,"  McGraw-Hill  Book  Co., 
Inc.,  New  York. 


174 


CHAPTER  XXVIII 


MISCELLANEOUS   DRAWINGS  AND  LISTS 


175 


STRUCTURE * 


UNIVERSITY    BRIDGE   COMPANY 

OFFICE  -BUILDING 


_  SKETCH, SHOP  AMD  SHIPPING  BfLL 


Holes  in  top  jj  drilled 


'///////A     VS/A     Y//////////////''''''' 

\7\core          ^Bottom  not finished 
^  l'o//omedForgroufii 


•Honed  For  grouting 


CBI 


325 


__.ILL  MADE  .V A.J3.T. JU.TI-J/L/J8 .CONTRACT  »O._33OO_. 

BILL  CHECKED  BT QiT^B._ DATK__^2.^^?__  .  SHEET  NUMta       C-C 


UNIVERSITY   BRIDGE   COMPANY 


3'thread 
-« 1- 


3  thread 


X2 


X3 


10 


\6 


XI 


SwayRoOsf* 


Hex,  nuts 


Hex.nufs 


Hex.  nuts 


Hex.  nuts 


X7 


© 


Hex.  nuts 


Hex,  nuts 


22 


20  m 


70 


6J_ 


sol 
5/ 

s\ 


BILL  MADE  BY «^*f: D*TUZ_/K_«* CONTRACT  N0._ 

o/lO  C                                                    H  TO                                                O  —ff    I A 
_f±,V.lS& BILL  CHECKED  VI '-  D^-li i*i DATfJ?. _/5_/S •*HKT  NUMIER 


Fig.  175  (a).   Combination  Sheet  with  Drawing. 


Fig.  175  (6).   Combination  Sheet  with  Small  Sketches. 


some  companies  require  them  for  all  rods;  but  usually  sufficient  informa-  center  lines.  Main  diagonal  rods  are  marked  in  the  usual  manner  with 
tion  can  be  given  if  the  rods  are  shown  conventionally  by  single  lines,  a  letter  X  followed  by  a  specific  number  (page  80  :  7).  It  is  imprac- 
as  in  the  figure.  It  is  assumed  that  dimensions  are  taken  along  the  tical  to  paint  the  mark  on  each  individual  sag  rod  or  tie  rod;  they  are 


176 


PART  II  —  STRUCTURAL  DRAFTING 


UNIVERSITY   BRIDGE   COMPANY 
WORCESTER  .,,ANCM 
™,CTU«     FURIVACE_BU/L_D!MG_  ___                                  tncmts  LIST 

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pieces 

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BILL  MADE  •L_HK£fit.£ 

BILL  CHECKED  tY  _V/--lC.£ 

Q//A  //Q                                              I  "7  74? 
QATC_*r/.C^l/S;  CONTHACTNO_i.C-^_O  

J)ATK  &/2O^/8                      JHEET  NUMBER  EF    ^ 

Fig.  176.   Erector's  List  of  Field  Rivets  and  Bolts. 

usually  shipped  in  bundles  and  the  bundles  are  marked.     In  case  rods 
become  mixed  before  they  are  used,  the  erector  must  identify  them  by 


direct  measurement.  If  a  rod  is  indicated  on  the  erection  diagram  by 
an  X  and  a  number,  the  erector  must  refer  to  a  list  of  rods  to  determine 
the  proper  length;  this  extra  step  may  be  avoided  except  in  the  case  of 
bent  rods,  if  all  straight  tie  rods  and  sag  rods  are  marked  according  to 
their  lengths.  Thus,  on  the  diagram  the  length  in  inches  of  one  rod  in 
each  panel  may  be  inscribed  in  a  circle,  as  shown  in  Fig.  156  or  Fig.  158; 
the  circle  is  used  to  distinguish  these  marks  from  others.  Since  the 
tie  rods  or  sag  rods  of  a  given  structure  are  usually  of  the  same  diam- 
eter, the  erector  simply  needs  to  know  the  required  lengths;  it  is  more 
convenient  for  him  to  find  the  lengths  where  the  rods  are  shown  on  the 
diagrams,  than  to  have  to  refer  to  a  separate  list.  The  lengths  of  tie 
rods  and  sag  rods  are  usually  made  in  multiples  of  3"  in  order  to  reduce 
the  number  of  different  sizes;  in  determining  the  lengths,  use  may 
be  made  of  the  dimensions  on  page  316.  For  the  weights  of  rods  see 
page  315. 

1.  A  summary  of  field  rivets  and  bolts  must  be  prepared  for  each 
contract  in  order  that  the  proper  number  of  each  size  may  be  shipped 
to  the  site  for  use  in  erection.     Before  this  summary  can  be  made,  a 
detailed  "erector's  list  "  must  be  prepared  to  show  the  number  and  the 
size  of  the  rivets  to  be  used  in  each  connection.     To  have  each  connec- 
tion provided  for  once,  and  only  once,  it  is  well  to  have  one  man  list 
the  rivets  for  a  whole  structure  or  for  a  definite  portion  of  it;  he  should 
work  systematically  to  avoid  duplication.     Perhaps  the  best  plan  is 
to  take  one  sheet  at  a  time,  and  to  list  only  those  rivets  by  which  each 
member  on  that  sheet  is  connected  to  the  supporting  members.     The 
rivets  for  all  members  which  bear  the  same  shipping  mark  should  be 
listed  together,  and  the  rivets  for  similar  members  may  be  combined 
whenever  this  can  be  done  conveniently  without  adding  to  the  burdens 
of  the  erector. 

2.  A  typical  erector's  list  of  field  rivets  and  bolts  is  shown  in  Fig.  176; 
this  provides  for  the  connection  of  the  knee  braces  in  Fig.  140  and  of 
all  the  members  in  Fig.  147  to  the  columns  of  Figs.  135  and  137.     The 
erection  diagram  of  Fig.  156  should  be  used  as  a  guide  in  determining 
the  relative  positions  of  the  members.     A  rivet  is  made  with  one  head 
in  place.     The  shank  should  be  long  enough  to  extend  through  the  parts 
to  be  connected  far  enough  to  provide  sufficient  metal  for  the  forma- 


CHAPTER  XXVIII 


MISCELLANEOUS  DRAWINGS  AND   LISTS 


177 


tion  of  the  second  head  and  for  the  upsetting  of  the  shank  to  fill  the 
enlarged  hole  (page  30  :  4).  Rivets  commonly  used  in  structural 
work  are  either  "button  head"  or  "countersunk"  (page  40  :  6);  both 
heads  may  be  alike,  or  one  may  be  button  and  the  other  countersunk. 
The  length  of  a  button  head  rivet  is  measured  from  the  under  side  of  the 
head ;  the  length  of  a  countersunk  rivet  is  the  extreme  length  overall.  The 
"grip  "  of  a  rivet  is  the  total  thickness  of  metal  through  which  it  must 
pass,  i.e.,  the  sum  of  the  thicknesses  of  the  parts  connected.  The 
length  of  a  rivet  is  the  sum  of  the  grip  and  the  extra  length  required  for 
upsetting.  The  thicknesses  of  I-beam  and  channel  flanges  at  the 
rivet  lines  are  shown  in  the  tables  on  pages  298  to  302.  The  lengths 
of  rivets  vary  slightly  according  to  the  shapes  of  the  heads  adopted 
as  standard  by  different  companies.  Tables  are  used  to  determine 
the  proper  lengths  of  rivets  for  different  grips.*  These  tables  are 
usually  arranged  for  grips  varying  by  eighths  of  an  inch.  The 
grips  for  both  rivets  and  bolts  are  usually  recorded  to  the  nearest 
sixteenth,  but  this  is  unnecessary  unless  one  is  likely  to  be  substituted 
for  the  other;  for  rivets,  grips  in  sixteenths  should  be  increased  tV 
before  the  lengths  are  found.  Care  should  be  taken  to  differentiate 
between  countersunk  and  button  head  rivets;  more  metal  is  required 
to  form  a  button  head  than  a  countersunk  head.  It  is  well  to  record 
the  lengths  of  all  countersunk  rivets  as  soon  as  the  grips  are  recorded, 
being  careful  to  place  them  in  the  proper  column.  It  is  usually  more 
convenient  to  omit  the  lengths  of  button  head  rivets  until  one  or  more 
pages  of  the  erector's  list  are  otherwise  complete,  when  they  can  all  be 
recorded.  The  bolts  are  listed  upon  the  same  form  as  the  rivets,  but 
the  style  of  head  (button,  square,  or  hexagonal)  and  the  style  of  nut 
(square  or  hexagonal)  should  be  indicated  as  shown.  The  length  of  a 
bolt  is  measured  from  the  under  side  of  the  head;  it  should  be  a  multiple 
of  j  inch.  A  bolt  should  extend  from  T'ff  to  j  inch  beyond  the  nut  to 
insure  the  full  bearing  of  all  the  threads  in  the  nut.  The  thickness  of 
a  nut  is  the  same  as  the  diameter  of  the  bolt  with  which  it  is  used. 
When  washers  are  used,  a  bolt  should  be  made  correspondingly  longer. 

*  The  standards  of  the  American  Bridge  Company  are  given  in  the  "Pocket  Com- 
panion" of  the  Carnegie  Steel  Company,  and  in  Ketchum's  "Structural  Engineers'^ 
Handbook,"  McGraw-Hill  Book  Co.,  Inc.,  New  York. 


UNIVERSITY   BRIDGE   COMPANY 

WORCESTER „»„«:„ 


HADE  IT. ^ DATE . CO»T«ACT  HO- 

ULL  CHECKED  1Y  _«/!_/£_£_• ^JMK_^/?^/J§_ SHEET  NUNtM  C 


Fig.  177.   Summary  of  Field  Rivets  and  Bolts. 

1.   A  summary  of  field  rivets  and  bolts  is  made  on  a  form  similar  to 
the  erector's  list  except  that  blanks  for  weights  and  shipments  are  sub- 


178 


PART  II  —  STRUCTURAL  DRAFTING 


stituted  for  the  grip  and  the  list  of  members  connected,  as  shown  in 
Fig.  177.  All  the  field  rivets  and  bolts  on  a  whole  contract  may  be 
summarized  in  one  list  unless  different  portions  of  a  structure  are  grouped 
under  different  shipments,  when  the  rivets  may  be  divided  accordingly. 
The  number  of  each  different  size  and  style  of  rivet  and  bolt  may  be 
determined  by  means  of  a  sheet  ruled  into  columns;  each  item  from 
the  erector's  lists  may  be  recorded  in  the  proper  column  and  then  each 
column  may  be  totaled.  These  totals  should  be  increased  by  certain 
percentages  in  order  to  allow  for  waste,  for  miscounts,  and  for  mis- 
placements. These  percentages  should  be  greater  for  small  numbers 
in  order  to  provide  a  safe  margin,  as  indicated  in  the  following  table:  * 


Percentage  to  be  added. 

Rivets. 

Bolts. 

1  to    10 

100 

50 

11  to    50 

50 

25 

51  to  100 

25 

12J 

101  to  500 

15 

U 

over  500 

10 

5 

In  the  illustration,  the  summary  has  been  made  simply  for  the  rivets 
and  bolts  shown  in  the  typical  erector's  list  and  not  for  the  whole  con- 
tract. The  weights  of  rivets  and  bolts  should  be  computed  only  when 
the  weight  of  the  other  steel  work  is  required.  The  weight  recorded 
is  the  total  weight  of  all  the  rivets  or  bolts  listed  on  one  line.  The 
weights  of  rivets,  bolts,  and  washers  are  tabulated  in  many  hand- 
books and  structural  company  standards.  The  tables  on  page  304  give 
*  Standards  of  the  American  Bridge  Company. 


the  weights  of  the  shanks,  the  heads,  and  the  nuts;  the  weight  of  the 
shank  can  be  multiplied  by  the  proper  length  and  combined  with  the 
weight  of  the  head  or  the  head  and  nut.  The  weight  of  a  washer  is 
approximately  three-tenths  of  the  product  of  the  thickness  in  inches 
by  the  net  area  in  square  inches;  the  holes  are  usually  \  inch  larger 
than  the  bolts. 

1.  Erection  Bolts.  —  As  soon  as  a  member  is  swung  into  the  proper 
position  in  a  structure  it  is  held  in  place  by  erection  bolts  put  in  some 
of  the  holes  of  the  field  connections;  after  the  remaining  holes  are 
riveted  these  bolts  are  replaced  by  rivets.  In  this  way  the  erection 
gang  is  enabled  to  make  greater  progress  for  they  do  not  have  to  wait 
for  the  rivets  to  be  driven;  special  gangs  of  riveters  drive  the  rivets. 
If  permanent  bolts  are  to  be  used,  the  erection  gang  may  use  permanent 
bolts  for  erection  so  that  they  need  not  be  replaced-;  these  permanent 
bolts  are  provided  in  suitable  lengths  as  explained  above.  The  tempo- 
rary fitting-up  or  erection  bolts  are  made  longer  than  permanent  bolts 
and  they  are  provided  with  washers.  The  washers  make  the  bolts 
more  serviceable  because  a  bolt  may  be  used  for  different  grips  by 
varying  the  number  of  washers;  incidentally  the  use  of  washers  facili- 
tates the  removal  of  the  bolts.  Not  all  structures  are  erected  by  the 
company  that  furnishes  the  material,  and  erection  bolts  should  not  be 
furnished  unless  specified.  Each  bolt  should  be  provided  with  two 
f-inch  washers,  and  the  lengths  should  vary  by  \  inch.  The  number 
should  be  based  upon  the  number  of  field  rivets  furnished.  For  build- 
ings and  miscellaneous  structures  the  number  for  each  grip  should  be 
about  30  per  cent  of  the  number  of  field  rivets;  for  bridges  this  should 
be  increased  to  50  per  cent,  or  even  80  per  cent  for  the  floor  systems 
and  the  tension  members  where  more  bolts  are  likely  to  be  lost. 


CHAPTER  XXIX 
CHECKING   AND   CORRECTING  DRAWINGS 

SYNOPSIS:  In  this  chapter  are  given  points  for  the  checker  to  consider  while  checking 
a  drawing.  These  points  should  also  be  anticipated  by  the  detailer  in  order  that  he 
may  guard  against  mistakes. 


1.  A  checker  is  a  person  who  "checks  "  or  approves  the  correct  por- 
tions of  a  drawing  and  indicates  the  mistakes  for  correction.     After 
these  mistakes  have  been  verified  and  corrected  by  the  detailer,  the 
checker  ascertains  that  all  corrections  have  been  made  and  then  signs 
the  drawing   to   show  that  he   has  assumed   responsibility  for  every 
detail,   every  figure,   and   every  note,  in   short  for  the  entire  draw- 
ing.    The   checker   is  usually  a  man  of  greater  experience  than  the 
detailer,  and   no   draftsman  is  allowed  to  check  the  work  of  others 
until  he  is  able  to  make  drawings  which  are  comparatively  free  from 
errors. 

2.  Not  all  Drawings  are  Completely  Checked.  —  Some  structural  com- 
panies have  fixed  policies  regarding  checking,  while  other  companies 
leave  to  the  chief  draftsman  or  the  squad  foreman  in  charge  of  a  given 
contract  the  decision  of  whether  or  not  the  drawings  for  that  contract 
shall  be  checked.     The  importance  of  careful  checking  depends  upon 
the  ability  and  the  skill  of  the  draftsman;   it  is  essential  for  the  draw- 
ings made  by  inexperienced  men.     The  importance  increases  with  the 
size  of  a  contract  and  the  number  of  draftsmen  engaged  upon  it,  because 
of  greater  difficulty  in  insuring  the  proper  agreement  between  the  draw- 
ings of  connecting  members.     A  checker  can  work  to  better  advantage 
than  the  detailer  because  the  drawings  of  connecting  members  are 
usually  farther  advanced  so  that  he  can  compare  the  completed  con- 
nections more  definitely.     The  majority  of  companies  have  all  their 
drawings  checked  because  they  are  unwilling  to  assume  the  risk  of 


serious  mistakes  which  might  be  made  if  only  one  draftsman  were 
responsible.  Since  no  draftsman  is  infallible  these  companies  believe 
that  every  drawing  should  be  the  product  of  two  minds.  Some  com- 
panies find  that  it  is  economical  to  have  all  drawings  made  by  experi- 
enced draftsmen  whose  work  is  comparatively  free  from  errors  without 
being  checked;  these  companies  maintain  that  occasional  mistakes  can 
be  rectified  at  a  smaller  cost  and  to  better  advantage  than  all  drawings 
can  be  checked,  particularly  for  structures  which  are  to  be  erected  within 
comparatively  short  distances  from  the  plant.  Perhaps  a  better  method 
would  be  to  have  the  main  dimensions,  the  strength  of  the  connections, 
and  the  spacing  of  all  holes  for  field  connections  checked,  but  not  the 
spacing  of  the  shop  rivets  or  the  sizes  of  component  parts  which  will 
necessarily  be  verified  in  the  shop.  Sometimes  a  "field  check"  of  an 
entire  contract  is  made  either  .instead  of  or  in  addition  to  the  usual 
checking.  Such  a  check  is  made  after  most  of  the  drawings  are  ready 
for  the  shop  but  before  any  of  the  members  are  shipped,  and  preferably 
before  the  shopwork  has  progressed  very  far.  The  object  of  this  check 
is  to  insure  the  proper  erection  of  the  structure,  and  it  includes  the 
checking  of  all  main  dimensions  and  all  field  connections;  it  should 
preferably  be  made  by  one  person.  A  field  check  should  be  unnecessary 
for  small  contracts,  but  it  may  be  desirable  for  large  contracts  (a)  when 
the  number  of  field  connections  is  relatively  large,  as  in  export  work; 
(6)  when  the  cost  of  field  changes  would  be  prohibitive  on  account  of 
inaccessibility  or  the  lack  of  facilities;  or  (c)  when  the  drawings  of 


179 


180 


PART   II  —  STRUCTURAL  DRAFTING 


connecting  members  have  been  made  by  a  large  number  of  datallers  and 
checked  by  several  checkers  all  working  simultaneously. 

1.  A  detailer  should  become  familiar  with  the  work  of  a  checker  and 
apply  the  checker's  methods  to  his  own  work  as  far  as  practical.     This 
is  especially  true  if  his  work  is  not  to  be  checked  by  another  person,  but 
no  drawing  should  be  submitted  to  a  checker  until  the  detailer  feels 
confident  that  it  is  comparatively  free  from  error.     He  should  never 
allow  a  mistake  of  which  he  is  aware  to  go  to  the  checker  uncorrected. 
A  beginner  is  judged  not  so  much  by  the  mistakes  he  makes  as  by  the 
mistakes  he  repeats.     A  man  who  profits  by  each  correction  which  is 
brought  to  his  attention  and  avoids  making  similar  mistakes  on  future 
drawings  will  soon  surpass  the  men  who  are  not  so  careful.     The  de- 
tailer will  find  that  many  of  the  suggestions  given  in  this  chapter  may 
be  applied  to  his  drawing  to  advantage  before  it  is  submitted  to  the 
checker.     Many  of  these  checks  may  be  made  at  a  glance,  and  they 
should  always  be  applied.     The  detailer  should  also  determine  each 
important  dimension  in  more  than  one  way  if  possible.     He  should 
never  divide  a  distance  into  rivet  spacing  or  other  subdivisions  without 
adding  all  the  dimensions  and   comparing   the  sum  with  the  proper 
total. 

2.  A  checker  should  work  systematically  so  that  he  will  not  miss  any 
portion  of  the  drawing.     He  should   collect  all   data   concerning  the 
member  or  members  shown  on  a  given  drawing,  and  make  sure  that 
nothing  is  overlooked.     It  is  not  sufficient  to  check  what  the  draftsman 
has  done,  but  it  is  especially  important  to  discover  his  errors  of  omission. 
A  good  checker  is  distinguished  from  a  poor  one  very  largely  by  his 
ability  to  detect  omissions.     The  checker  should' check  the  most  import- 
ant parts  of  a  drawing  first,  proceeding  logically  so  that  no  part  will  be 
checked  until  the  parts  upon  which  it  is  dependent  are  checked. 

3.  The  following  suggestions  show  the  more  general  points  to  be 
considered  in  checking  a  drawing,  arranged  approximately  in  logical 
order:  — 

(1)  General  Appearance:  see  that  the  general  arrangement  is  satis- 
factory; that  the  proper  views  are  used  to  show  the  member  to  the 
best  advantage;  that  all  views  bear  proper  relations  to  one  another; 
that  the  proper  scale  is  used  so  that  the  drawing  is  clear  and  not  crowded; 


and  that  not  too  many  different  members  are  combined  on  the  same 
drawing  thus  making  it  too  complicated. 

(2)  Main  Dimensions:    see   that  the  proper  type  of   connection   is 
provided  at  the  supports;    that  the  proper  clearances  are  allowed  for 
erection;    that  the  main  dimensions  are  given  conspicuously  in  such  a 
manner  that  they  will  be  of  most  service;    and  that  the  main  material 
is  billed  conventionally  in  accordance  with  the  main  dimensions  and 
with  the  design. 

(3)  Connections  at  Supports:   see  that  the  strength  of  the  rivets  and 
the  component  material  is  sufficient  to  carry  the  stresses;    that  the  size 
and  the  spacing  of  the  holes  for  the  field  rivets  correspond  to  those  in 
the  supporting  members;   and  that  the  material  is  properly  billed. 

(4)  Other  Connections:   see  that  provision  is  made  for  all  connecting 
members;   that  the  connections  are  properly  located;   that  the  number, 
the  size,  and  the  spacing  of  the  holes  for  the  field  rivets  correspond 
exactly  to  those  in  the  connecting  members;  that  all  connecting  members 
can  be  erected  without  interference;    and  that  all  material  is  properly 
billed. 

(5)  Lattice  Bars  and  Rivets:    see  that  all  lattice  bars,  batten  plates, 
and  rivets  are  properly  spaced  to  conform  to  the  specifications  and  to 
the  usual  rules;   that  all  rivets  and  bolts  are  so  located  that  they  can  be 
put  into  position;   that  sufficient  clearance  is  allowed,  if  possible,  so  that 
the  rivets  can  be  driven  by  machine;  that  rivets  which  should  be  counter- 
sunk or  flattened  are  properly  indicated;    and   that  necessary  stitch 
rivets  are  provided. 

(6)  Edge  Distances:  see  that  all  necessary  edge  distances  are  given, 
for  example,  those  which  will  prevent  interference  with  erection. 

(7)  Special    Cutting:    see  that    sufficient  dimensions  and  notes  are 
given  for  special  cutting  or  coping,  particularly  when  a  variation  will 
cause  interference  or  mar  the  appearance  of  the  finished  structure. 

(8)  Dimensions:  see  that  interdependent  dimensions  bear  the  proper 
relation  to  one  another;    that  the  distance  between  any  two  points  is 
the  same  when  obtained  by  adding  the  intervening  dimensions  on  any 
one  of  two  or  more  parallel  dimension  lines;    and  that  no  dimension 
lines  or  other  lines  or  points  appear  to  coincide  on  the  drawing  unless 
it  is  proper  that  they  should  coincide. 


itch 
i,  as 


CHAPTER  XXIX 


CHECKING  AND  CORRECTING  DRAWINGS 


181 


(9)  Milling:  see  that  all  surfaces  to  be  faced,  milled,  or  planed  are 
properly  marked. 

(10)  Notes:    see  that  all  notes  are  given  which  render  the  drawing 
clearer  or  more  definite,  such  as  "symmetrical  about  the  center  line  "; 
that  all  differences  between  members  which  are  combined  on  the  same 
drawing  are  clearly  noted;    and  that  all  loose  material  which  is  not  to 
be  shipped  separately  is  noted  "Bolted  for  shipment". 

(11)  Shipping  Marks:    see  that  each  member  is  provided  with  the 
proper  shipping  mark;   that  the  marks  correspond  to  the  marks  on  the 
erection  diagrams;   that  proper  distinction  is  made  between  rights  and 
lefts;   and  that  the  required  number  of  members  is  correct. 

(12)  Sizes  of  Rivets:    see  that   the  sizes  of  all   rivets,  bolts,  holes, 
and  washers  are  given  either  in  a  general  note  or  in  special  notes. 

1.  Indicating  Mistakes.  —  The  checker  should  indicate  all  mistakes 
so  that  the  draftsman  will  be  able  to  make  the  necessary  changes  without 
disturbing  the  checker's  notes.  See  Fig.  181.  These  notes  should  be 
preserved  until  the  checker  has  convinced  himself  that  all  changes 
have  been  made  correctly.  The  mistakes  may  be  indicated  either  on 
the  tracing  or  on  a  blueprint.  The  former  method  is  more  direct  and 
more  common;  it  is  also  quicker  because  the  checker  does  not  have  to 
wait  for  a  print  to  be  made,  and  the  draftsman  does  not  need  to  refer  to 
a  print  before  making  each  change  on  the  tracing.  The  blueprint 
method  is  used  when  a  permanent  record  of  the  checker's  marks  is 
desired. 

The  temporary  mark  of  the  checker  may  be  made  on  the  tracing  with  either  blue  or 
soft  black  pencil.  It  is  easier  to  maintain  a  sharper  point  on  the  black  pencil  than  on 
the  blue,  and  hence  the  figures  and  notes  need  not  be  made  so  large.  The  black  marks 
may  be  removed  more  readily  than  the  blue.  Marks  on  blueprints  may  be  made  sat- 
isfactorily with  either  black  or  yellow  pencils.  Red  pencils  should  not  be  used  on 
either  tracing  cloth  or  blue  prints.  The  red  marks  cannot  be  erased  easily  from  the 
cloth  —  in  fact  it  is  impossible  to  remove  some  of  them.  There  are  certain  combina- 
tions of  red  crayon  on  blue  prints  which  cause  unnecessary  eye  strain  on  account  of  an 
optical  illusion  which  makes  it  difficult  for  the  eye  to  focus  on  the  red  lines. 

A  freehand  ring  or  loop  drawn  around  a  dimension,  a  note,  or  a  whole 
detail  usually  signifies  that  the  enclosed  portion  is  incorrect.  A  line 
may  be  drawn  from  the  ring  to  a  convenient  clear  space  on  the  drawing 


where  the  correct  value  or  other  note  may  be  written  by  the  checker  so 
that  it  need  not  be  disturbed  by  the  draftsman  when  he  makes  that  or 
any  other  correction.  An  inked  ring  is  often  drawn  around  a  group  of 
holes  with  a  line  leading  to  a  special  note  (page  52  :  4),  but  in  order  to 
avoid  ambiguity  such  a  ring  should  not  include  figures  or  notes.  A 
penciled  ring  may  be  drawn  around  a  detail  which  is  likely  to  be  changed; 
such  a  ring  should  invite  suspicion  or  doubt,  and  no  use  should  be  made 
of  figures  or  other  data  taken  without  verification  from  within  the 
ring.  Accordingly  it  is  not-good  practice  to^encircle  any  dimension  or 

-x-x^&P  'wwaz*'  i      j\  j/rfy  0 

^ffi^A^W^  -^' 


Fig.  181.   Method  of  Indicating  Mistakes. 

note  unless  it  is  either  wrong  or  doubtful  because  of  incomplete  or 
revised  information. 

2.  Check  Marks.  In  checking  a  drawing  a  checker  usually  places  a 
dot  or  a  v-shaped  check  mark  over  each  correct  dimension  or  note 
(Fig.  181).  These  check  marks  indicate  his  progress  and  make  him 
less  liable  to  overlook  parts  of  the  drawing;  they  are  of  special  value  on 
complicated  drawings.  Check  marks  may  be  made  with  a  pencil  and 
later  erased,  or  they  may  be  made  permanently  in  red  or  blue  ink  for 
future  record.  If  ink  is  used,  some  checkers  place  the  check  marks 
underneath  corrected  figures  to  distinguish  them  from  those  which  were 
originally  correct. 


182 


PART   II  —  STRUCTURAL   DRAFTING 


1.  Back-checking.  —  A  draftsman  should  never  change  a  drawing 
according  to  the  checker's  notes  until  he  is  convinced  that  such  changes 
should  be  made.     Unless  he  "back-checks  "  or  verifies  each  correction 
before  making  it,  certain  parts  of  the  drawing  are  left  unchecked,  the 
value  being   the   checker's  instead   of   the  detailer's.     No   checker  is 
infallible,  and  every  sheet  that  is  supposed  to  be  checked  should  be 
completely  checked.     A  checker  usually  indicates  the  values  which  he 
believes  to  be  correct;   this  is  the  simplest  method  for  him  to  use.     It 
is  also  the  most  convenient  method  for  the  detailer  who  back-checks 
conscientiously.     Some  checkers  wish  to  insure  back-checking  by  with- 
holding the  correct  values  until  after  the  draftsman  has  supplied  them. 
These  checkers  indicate  mistakes  for  the  draftsman  but  record  the  cor- 
rect values  on  a  blueprint  or  in  a  book  for  their  own  use  in  checking 
the  corrected  drawing.     For  convenience  in  identification   they  may 
number  the  mistakes  consecutively. 

2.  In  checking  students'  drawings  it  is  well  for  the  instructor  to 
indicate  the  mistakes  so  that  the  students  will  have  to  determine  the 
correct  values  themselves  before  they  can   correct  the  drawings.     A 
practical  method  which  has  proven  successful  in  the  author's  classes  is 
to  indicate  not  the  correct  values,  but  the  reference  numbers  to  para- 
graphs which  will  suggest  the  nature  of  the  mistakes.     This  may  result 
in  more  work  for  the  instructor  but  not  as  much  more  as  might  be 
imagined.     The  mistakes  on  the  similar  drawings  of  a  whole  class  which 
are  corrected  at  any  one  time  cover  only  a  limited  range;  most  of  the  mis- 
takes are  made  by  several  men  so  the  paragraph  numbers  are  soon 
memorized.     The  method  may  be  simplified  by  spreading  the  drawings 
out  on  a  large  table  and  checking  one  connection  or  other  small  portion 
of  all  the  drawings  before  another  portion  is  checked.     The  extra  burden 
on  the  instructor  seems  justified  by  the  benefit  to  the  student.     He 
gets  a  much  better  understanding  of  each  correction  and  he  is  less 
liable  to  repeat  the  same  mistake.     His  increased  familiarity  with  the 


ne 


text  makes  the  book  more  valuable  for  future  reference.  It  is  g< 
practice  for  the  students  to  check  each  other's  drawings  and  one  ques- 
tion on  a  test  or  examination  may  well  be  devoted  to  the  correction  of 
a  drawing  which  contains  many  mistakes.  In  this  work  a  student's 
grade  should  be  based  upon  his  net  score,  the  number  of  mistakes  he 
makes  being  deducted  from  the  number  which  he  detects. 

3.  Corrections.  —  After  the  draftsman  has  verified  all  corrections 
should  carefully  erase  the  incorrect  portions  of  his  drawing  and  replace 
them  with  the  correct.     The  figures  should  not  be  crossed  out  and  new 
ones  should  not  be  superimposed  as  in  the  unchecked  field   notes  of 
surveying.     There  is  no  necessity  for  preserving  the  incorrect  figures 
of  the  draftsman  after  the  sheet  has  been  checked  and  both  the  checker 
and  the  draftsman  are  convinced  that  the  figures  are  wrong.     If  these 
figures  were  retained,  the  appearance  of  the  drawing  would  be  marred, 
the  drawing  would  be  made  less  distinct,  and  the  draftsman's  mistakes 
would  be  exposed  to  all  who  use  the  drawing.     It  is  important  that  all 
changes  be  made  without  disturbing  the  checker's  marks.     If  any  note 
of  the  checker  is  erased  accidentally  the  draftsman  should  pencil  a  con- 
spicuous question  mark  near  the  corresponding  change  to  draw  the 
attention   of  the   checker   to   the   change.     The   checker  may   simply 
check  the  changes  and  then  assume  responsibility  for  the  drawing  by 
signing  his  initials  to  the  sheet.     If  his  marks  were  erased  he  would 
have  to  recheck  much  or  all  of  the  drawing  before  he  could  be  sure  that 
it  was  correct,  particularly  if  much  time  had  elapsed  since  he  first 
checked  the  drawing. 

4.  Revisions.  —  If  changes  are  made  after  prints  have  been  issued, 
the  prints  must  be  revised  or  replaced  by  new  prints.     In  either  case  the 
changes  should  be  indicated  conspicuously.     If  the  old  prints  are  re- 
vised with  black  ink  or  colored  crayon  the  changes  are  apparent.     If 
new  prints  are  issued  the  revised  portions  should  be  underscored  or 
otherwise  marked  with  colored  crayon  to  attract  attention. 


PART  III  — THE  DESIGN  OF  DETAILS 


CHAPTER  XXX 
SHEAR  AND  BENDING  MOMENT 

SYNOPSIS:  Every  structural  draftsman  should  know  how  to  design  a  beam  or  a  girder 
to  satisfy  different  requirements.  The  design  is  comparatively  simple  after  the  shear 
and  the  bending  moment  are  known.  The  first  step  is  to  find  the  shear  and  the  bend- 
ing moment  under  different  conditions. 


1.  The  terms  "  shear  "  and  "  bending  moment  "  are  convenient  expres- 
sions for  certain  quantities  which  are  used  repeatedly  in  the  design  of 
beams,  girders,  and  similar  members.     Their  definition  presupposes  the 
knowledge  of  forces  and  moments.    Shear  and  bending  moment  depend 
upon  the  magnitudes  and  relative  positions  of  external  forces,  such  as  the 
applied  loads  and  the  reactions  at  the  supports.    Since  the  majority  of 
external  forces  for  which  beams  are  designed  are  either  horizontal  or 
vertical,  it  is  convenient  to  resolve  all  other  forces  into  horizontal  and 
vertical  components.     Any  other  system  of  rectangular  coordinate  axes 
may  be  chosen  if  preferred,  as,  for  example,  when  inclined  beams  are 
subjected  to  normal  forces. 

2.  Principles.  —  In   Statics  a  system  of  forces  in  equilibrium  must 
satisfy  three  conditions,  viz.:    the  algebraic  sum  of  the  horizontal  com- 
ponents of  all  the  forces  must  equal  zero;  the  algebraic  sum  of  the  vertical 
components  of  all  the  forces  must  equal  zero;  and  the  algebraic  sum  of  the 
moments  of  all  the  forces  about  any  point  of  moments  must  equal  zero. 
These  three  equations  of  equilibrium  are  commonly  indicated  thus:  S  H  =  0, 
SF  =  0,  and  S  M  =  0.    In  this  book  they  will  be  referred  to  as  the  "  H 
equation,"  the  "  V  equation,"  and  the  "  M  equation,"  respectively. 

3.  Signs.  — •  In  order  to  obtain  algebraic  sums  it  is  necessary  to  adopt 
system  of  signs  for  components  and  moments.     Any  system  may  be 


used  provided  that  system  is  followed  consistently  throughout  a  given 
problem.  It  is  convenient  to  adhere  to  one  system  in  all  problems  in 
order  to  avoid  confusion  and  to  eliminate  one  source  of  error.  In  this 
book  all  horizontal  components  toward  the  right,  all  vertical  components 
upward,  and  all  moments  of  forces  which  tend  to  cause  clockwise  rota- 
tion about  the  point  of  moments  are  considered  positive.  Conversely, 
components  toward  the  left  or  downward,  and  moments  of  forces  which 
tend  to  cause  counterclockwise  rotation  are  considered  negative. 

4.  Forces  Considered.  —  The  equations  of  equilibrium  may  be  applied 
to  a  beam  as  a  whole,  or  to  a  portion  of  a  beam.  When  the  whole  beam 
is  considered,  all  the  external  forces  which  act  on  the  beam  must  be  in 
equilibrium.  Thus,  any  unknown  external  force,  such  as  the  reaction 
at  a  support,  is  found  by  applying  the  principles  of  equilibrium  to  the 
beam  as  a  whole.  When  only  a  portion  of  a  beam  is  considered,  the 
external  forces  acting  upon  that  portion  are  not,  as  a  rule,  in  equilibrium, 
but  they  are  held  in  equilibrium  by  the  internal  forces  or  stresses  which 
act  in  the  beam.  For  convenience,  the  external  forces  on  a  portion  or 
segment  of  a  beam  are  first  considered  and  quantities  termed  "  shear  " 
or  "  bending  moment "  are  obtained;  similar  expressions  are  found  from 
the  internal  forces  and  the  two  combined  must  satisfy  the  equations  of 
equilibrium.  The  consideration  of  the  internal  forces  depends  upon  the 


183 


184 


PART  III  — THE   DESIGN  OF  DETAILS 


form  of  the  beam  and  the  material;    this  is  a  matter  of  design  and  is 
treated  in  Chapters  XXXI  and  XXXIII,  pages  197  and  218. 

1.  The  "  shear  "  on  a  segment  of  a  beam  is  the  algebraic  sum  of  all  the 
external  forces  which  act  upon  that  segment.     It  is  not  a  force  but  a  sum 
of  forces;  it  is  not  the  sum  of  all  the  external  forces  on  the  beam  (which 
would  be  zero)  but  the  sum  of  those  forces  which  are  on  the  segment. 
This  sum  cannot  be  considered  to  act  at  any  one  point  or  at  any  one 
cross  section,  although  the  internal  forces  which  act  at  a  given  cross 
section  must  be  sufficient  to  resist  this  sum  or  shear.    It  is  better  to  speak 
of  "  the  shear  for  a  section  taken  at  a  given  point  "  meaning  the  shear 
on  a  segment  of  the  beam  made  by  this  section.    Such  a  section  should 
not  coincide  with  the  line  of  action  of  any  force,  but  it  may  be  considered 
to  pass  infinitely  close  to  the  force  on  either  side  so  that  the  whole  force 
is  either  on  one  segment  or  the  other.    For  any  section,  the  shear  on  one 
segment  is  numerically  equal  to  the  shear  on  the  other  segment  but  with 
opposite  sign;    this  is  necessarily  so  because  the  algebraic  sum  of  the 
two  must  equal  zero  to  satisfy  the  V  equation  of  equilibrium  applied 
to  the  whole  beam. 

2.  The  "  bending  moment "  at  any  point  of  a  beam  is  the  algebraic  sum 
of  the  moments  of  all  the  external  forces  at  the  left  of  that  point,  the  latter 
being  taken  as  the  point  of  moments.     A  cross  section  at  the  point  of 
moments  cuts  the  beam  into  two  segments,  only  one  of  which  is  considered 
in  finding  the  bending  moment.     The  bending  moment  found  from  the 
forces  on  the  left-hand  segment  is  numerically  equal  to  the  bending  mo- 
ment found  from  the  forces  on  the  right-hand  segment  but  opposite  in 
sign;  thus  the  algebraic  sum  of  the  two  equals  zero  to  satisfy  the  M  equa- 
tion of  equilibrium  applied  to  the  whole  beam.    It  is  less  confusing  for 
the  beginner  always  to  use  the  left-hand  segment;  he  is  less  liable  to  use 
the  wrong  signs.     It  is  of  course  simpler  to  use  the  segment  which  has 
the  smaller  number  of  forces,  but  until  the  student  has  become  proficient 
it  is  better  for  him  to  use  the  left  segment.    In  case  the  right-hand  seg- 
ment contains  a  smaller  number  of  forces  the  whole  beam  may  be  turned 
around;    that  is,  it  may  be  considered  to  be  viewed  from  the  opposite 
side  when  the  sketch  is  drawn.    It  is  imperative  that  the  units  of  bending 
moments  be  expressed  in  every  case.     Bending  moments  in  pound-feet 
and  in  pound-inches  are  both  used  so  extensively  that  failure  to   dis- 


tinguish between  them  is  the  cause  of  many  serious  mistakes.  In  this 
book  MB  and  mz  are  used  to  indicate  bending  moments  in  pound-feet 
and  pound-inches,  respectively. 

3.  The  use  of  formulas  for  finding  shear  or  bending  moment  should  be 
reduced  to  a  minimum.    The  fundamental  principles  of  shear  and  bend- 
ing moment  are  so  easily  applied  to  beams  under  usual  conditions  that; 
it  is  useless  to  attempt  to  memorize  or  even  recognize  the  many  formulas 
so  often  used  for  beams  under  different  forms  of  loading.    It  is  unnecessary 
to  differentiate  between  simple  and  cantilever  beams  (page  83  :  1)  since; 
the  same  methods  are  applicable.    The  extensive  use  of  formulas  makes 
a  man  either  dependent  upon  his  memory  to  a  dangerous  degree  or  else 
a  slave  to  a  handbook.    A  student  who  constantly  reverts  to  a  fundamenta 
principle  as  simple  as  "  the  algebraic  sum  of  the  forces  (or  the  moments' 
on  the  left  of  a  given  section  "  in  finding  shear  or  bending  moment  wil 
probably  never  forget  how  to  solve  a  similar  problem  without  a  hand 
book.     Furthermore,  he  can  solve  the  problems  more  surely  and  aboui 
as  quickly  in  this  way  as  if  he  substituted  in  formulas  which  cannot  lonj 
be  retained  in  the  memory.    Formulas  are  serviceable  in  the  solution  o 
beams  with  fixed  ends  or  continuous  beams  with  more  than  two  sup 
ports  because  the  underlying  theory  is  too  complex  to  be  developed  fo 
every  problem.     Certain  short  cuts  will  suggest  themselves  to  the  mai 
who  has  a  large  number  of  similar  problems  to  solve,  but  for  the  mos 
part  they  should  be  avoided  by  the  student.     In  no  case  should  a  mai 
use  a  short-cut  formula  unless  he  can  readily  derive  it. 

4.  Sketches.  —  For  every  beam  a  single-line  sketch  should  be  drawi 
upon  which  are  shown  all  external  forces,  including  the  loads  and  thi 
resultant  reactions  at  the  supports.     The  magnitude  and  direction  o 
each  known  force  should  be  recorded,  as  well  as  all  dimensions  necessar 
to  locate  each  point  of  application.     The  remaining  magnitudes  an< 
directions  should  be  recorded  as  soon  as  determined.    The  reactions  of  ; 
simple  beam  are  considered  to  act  at  the  centers  of  the  supports,  am 
the  effective  length  is  the  distance  from  center  to  center  of  supports 
A  beam  which  is  supported  at  one  end  only  must  have  that  end  imbeddei 
in  a  wall  or  otherwise  fixed.    The  reaction  is  not  a  single  force,  for  obvi 
ously  no  single  force  applied  at  one  end  could  hold  the  beam  in  equilibrium 
At  least  two  forces  are  required,  either  parallel  or  non-parallel.     If 


[f  th 


CHAPTER  XXX 


SHEAR  AND  BENDING  MOMENT 


185 


tion  of  what  the  result  signifies.  In  case  a  separate  sketch  is  required  for 
any  step  it  may  be  drawn  at  the  right  of  the  description.  Thus,  in  general, 
each  step  is  completed  on  one  line.  It  is  of  great  advantage  to  instructors 
to  have  all  students  arrange  their  work  uniformly.  It  is  of  advantage 
to  everyone  to  arrange  his  work  so  that  he  or  anyone  else  can  readily 
find  the  result  of  any  step,  what  that  result  means,  and  how  it  was  ob- 
tained. These  results  are  more  conspicuous  if  tabulated  at  one  side  of 
the  page  instead  of  being  mixed  in  with  other  work.  The  advantage 
of  having  the  results  at  the  left  is  to  leave  no  space  between  the  results 
and  the  corresponding  indications  of  the  computation;  this  would  be 
difficult  to  effect  if  the  results  were  placed  at  the  right,  because  one  cannot 
anticipate  how  much  space  the  computation  and  the  description  will 
require. 

2.  Reactions.  —  Concentrated  loads.  The  first  step  in  finding  either 
the  shear  or  the  bending  moment  is  to  determine  all  the  external  forces, 
or  at  least  all  that  will  be  needed.  No  reactions  need  be  found  for  beams 
which  are  supported  at  one  end  only,  because  the  shear  and  the  bending 
moment  may  be  determined  without  them.  For  a  system  of  parallel 
forces  there  cannot  be  more  than  two  unknowns.  Usually  the  lines  of 
action  of  all  the  forces,  and  the  magnitude  of  all  but  one  or  two  are  known ; 
however  the  two  unknowns  may  be  the  line  of  action  of  one  force  (in- 
cluding the  point  of  application)  and  the  magnitude  of  one  force,  not 
necessarily  the  same  force.  The  unknowns  are  commonly  the  magni- 
tude (and  direction)  of  the  reactions  at  the  supports.  The  beam  is 
treated  as  a  whole  and  all  the  external  forces  are  considered  to  be  in 
equilibrium.  Any  inclined  forces  may  be  resolved  into  components  so 
that  the  horizontal  (or  other)  components  are  in  the  same  line  of  action; 
by  taking  the  points  of  moments  in  this  line  of  action  the  problem  be- 
comes similar  to  the  more  usual  case  of  a  horizontal  beam  with  vertical 
forces.  In  the  remainder  of  this  chapter  only  horizontal  beams  with 
vertical  forces  will  be  considered.  The  principles  may  be  readily  adapted 
to  vertical  beams  with  horizontal  forces,  or  even  inclined  beams  with 
inclined  forces.  When  there  are  no  horizontal  forces  there  can  be  no 
use  of  the  H  equation.  The  V  equation  cannot  be  used  alone  if  there 
are  two  unknowns.  The  M  equation  involves  two  unknowns  unless 
the  point  of  moments  is  chosen  in  the  line  of  action  of  one  of  the  unknown 


180 


PART  III  — THE   DESIGN   OF  DETAILS 


forces.  When  the  point  is  so  chosen  the  lever  arm  and  hence  the  moment 
of  this  unknown  becomes  zero,  and  the  magnitude  of  the  other  unknown 
may  be  determined  from  a  single  equation.  Similarly,  by  taking  the 
point  of  moments  in  the  line  of  action  of  the  force  just  found,  the  second 
unknown  may  be  found  from  another  M  equation.  The  sign  which 
results  from  the  solution  of  the  M  equation  is  not  the  sign  of  the  force 
but  of  its  moment.  The  direction  of  the  force  must  be  found  accord- 
ingly, with  due  consideration  of  the  point  of  moments.  This  is  of  special 
importance  in  cantilever  beams  for  the  direction  of  the  reactions  cannot 
be  determined  by  inspection.  The  V  equation  may  be  used  as  a  check. 
The  second  unknown  might  be  found  from  the  V  equation  after  the 
first  unknown  is  determined,  but  its  accuracy  would  be  dependent  upon 
the  accuracy  of  the  first  unknown.  By  using  the  M  equation,  each  un- 
known is  determined  from  the  original  data  independently.  It  is  good 
practice  to  avoid  the  use  of  computed  values  when  original  data  can  be 
used  equally  well,  because  an  error  in  the  first  value  does  not  affect  the 
second.  As  a  student  becomes  proficient  he  may  indicate  the  result  and 
the  solution  for  each  reaction  upon  a  single  line,  as  on  page  192  :  1  and  sub- 
sequent pages.  He  should  also  be  on  the  lookout  for  symmetrical  loads 
for  which  each  of  two  reactions  is  equal  to  one-half  the  sum  of  the  loads. 
1.  The  three  illustrative  problems  which  follow  show  how  reactions, 
shears,  and  bending  moments  may  be  found  for  typical  beams  with  con- 
centrated loads. 

FIRST   PROBLEM SIMPLE   BEAM 


1000 


e 


2000 

4 


1400 

s    I 


\RL=I900  2500 =/?„? 

Fig.  186  (a). 

To  find  the  reactions  (beam  treated  as  a  whole): 

0  =  RL  X  18  -  1000  X  14  -  2000  X  8  -  1400  X  3    (point    of    mo- 
ments at  RR) 
+  1,900#  =  RL  (clockwise  means  upward) 

0  =  1000  x  4  +  2000  x  10  +  1400  X  15  +  RR  X  18  (point  of  mo- 
ments at  RL) 
—  2,500#  =  RR  (counterclockwise  means  upward) 

0  =  1900  -  1000  -  2000  -  1400  +  2500  =  check. 


To  find  the  shear: 

+1,900#  =  RL  =  shear  for  a  section  between  RL  and  the  1000  load. 
+900#  =  +1900  -  1000  =  shear  for  a  section   between 

the  1000  and  2000  loads 
-1,100#  =  +1900  -  1000  -  2000  =  shear    for    a    section 

between  the  2000  and  1400  loads 
-2,500#  =  +1900  -  1000  -  2000  -  1400  =  shear     for     a 

section  between  the  1400  load  and  RR. 

These  values  may  be  checked  from  the  right-hand  segments  as  follows 
(see  page  184  :  1) : 

-1,900#  =  -1000  -  2000  -  1400  +  2500 

_900#  =  -2000  -  1400  +  2500 
+1,100#  =  -1400  +  2500 
+2,500#  =  RR. 

To  find  the  bending  moment: 

7,600#ft.  =  1900  x  4  =  MB  at  the  1000  load 

13,000#ft.  =  1900  x  10  -  1000  x  6  =  MB  at  the  2000  load. 

7,500#ft.  =  1900  x  15  -  1000  x  11  -  2000  x  5  =  MB  at  the  1400  load. 

These  values  may  be  checked  from  the  right-hand  segments  as  follows: 

-  7,600#ft.  =  2000  x  6  +  1400  X  11  -  2500  X  14 

-13,000#ft.  =  1400  X  5  -  2500  X  8 

-7,500#ft.  =  -2500  x  3. 

SECOND   PROBLEM  —  CANTILEVER   BEAM 


1000 


•2000 


\RL=2750       7SO  =  RS\ 

Fig.  186  (6). 

To  find  the  reactions  (beam  treated  as  a  whole): 

tO  =  -1000  X  18  +  RL  X  12  -  2000  x  8  +  500  X  2  (point 

ments  at  RR) 
+2,750#  =  RL  (clockwise  means  upward) 

0  =  -1000  x  6  +  2000  x  4  +  RR  x  12  +  500  x  14  (point  of  mo 

ments  at  RL) 
-750#  =  RR  (counterclockwise  means  upward) 

0  =  -1000  +  2750  -  2000  +  750  -  500  =  check. 


CHAPTER  XXX 


SHEAR  AND  BENDING  MOMENT 


187 


00 


1000 


2750 
2000 


To  find  the  shear: 

-1,000#=   shear  for  a  section  between  the  1000  load  and  RL 
+1,750#  =  -1000  +  2750  =  shear  for  a  section  between  RL  and  the 

2000  load 
-250#  =  -1000  +  2750  -  2000  =  shear  for  a  section 

between  the  2000  load  and  RR 
+500#  =  -1000  +  2750  -  2000  +  750  =  shear     for     a 

section  between  RR  and  the  500  load. 
To  find  the  bending  moment: 
-6,000#ft.  =  -1000  X  6  =  MB  at  RL 
+l,000#ft.  =  -1000  x  10  +  2750  X  4  =  MB  at  the  2000  load. 
-1.000#ft.  =  -1000  x  18  +  2750  X  12  -  2000  X  8  =  MB  at 

wav 

BB. 

THIRD  PROBLEM — CANTILEVER  BEAM  SUPPORTED  AT  ONE  END  ONLY 

« 

1000      800  V/n 

I    4   I      e     M 


Reactions  not  required.  Fig.  187  (a). 

To  find  the  shear: 
-1,000#  =  shear  for  a  section  between  the  1000  and  800 

loads 
-1,800#  =  -1000  -  800  =  shear  for  a  section  between  the 

800  load  and  the  wall 
To  find  the  bending  moment : 
-4,000#ft.  =  -1000  X  4  =  MB  at  the  800  load 
-14,800#ft.  =  -1000  X  10  -  800  X  9  =  MB  at  the  face  of  the  wall. 

1.  Uniformly  Distributed  Loads.  —  Some  loads  are  distributed  uni- 
formly along  a  beam  instead  of  applied  at  points  of  concentration.  The 
weights  of  the  beams  and  the  weights  of  superimposed  floors  are  examples 
of  such  loads.  Certain  other  loads,  such  as  tracks  or  crowds  of  people, 
are  for  convenience  considered  uniformly  distributed.  The  simplest  way 
to  treat  this  form  of  loading  is  to  make  temporary  substitutions  of  equiva- 
lent concentrated  loads.  One  substitution  may  be  made  in  finding  the 
reactions,  but  a  different  substitution  must  be  made  in  finding  each 
different  shear  or  bending  moment.  Uniformly  distributed  loads  are 
represented  by  rectangles,  the  lower  edges  of  which  are  the  single  lines 


representing  the  beams.  For  each  step  a  section  should  be  indicated  on 
the  original  sketch.  In  finding  a  reaction,  this  section  passes  through  the 
point  of  moments;  in  finding  a  shear  this  section  is  the  section  for  which 
the  shear  is  taken;  in  finding  a  bending  moment  this  section  passes 
through  the  point  where  the  bending  moment  is  required,  i.e.,  the  point 
of  moments.  For  each  different  section  a  separate  sketch  should  be 
drawn  of  one  segment  of  the  beam  (usually  the  left,  page  184  :  2)  showing 
clearly  the  portion  of  the  uniformly  distributed  load  on  thaff  segment. 
A  second  sketch  should  be  drawn  in  which  this  portion  of  the  uniformly 
distributed  load  is  replaced  by  a  single  equivalent  concentrated  load 
applied  at  the  center  of  gravity  of  this  portion  of  the  uniform  load  on 
the  segment.  These  equivalent  loads  should  never  be  shown  on  the  same 
sketch  with  the  uniform  loads  because  they  do  not  both  act  at  the  same 
tune.  It  is  well  to  indicate  these  equivalent  loads  by  forces  below  the 
beam  line  to  distinguish  them  from  actual  concentrated  loads  which  are 
superimposed.  The  importance  of  drawing  these  separate  sketches 
should  not  be  overlooked.  A  very  common  mistake  is  to  draw  one  sketch 
for  finding  a  reaction  and  to  use  the  same  sketch  for  finding  a  shear  or  a 
moment;  this  gives  entirely  different  results.  The  sketch  used  in  finding 
a  shear  may  be  used  in  finding  a  bending  moment,  provided  the  section 
is  taken  at  the  same  point. 

2.  The  following  illustrative  problems  show  how  reactions,  shears,  and 
bending  moments  may  be  found  for  typical  beams  with  uniformly  dis- 
tributed loads.  More  commonly  these  loads  extend  the  full  length  of  the 
beam  (see  next  paragraph);  but  the  same  method  is  applicable. 

FIRST   PROBLEM SIMPLE    BEAM 


a -100  H/ft. 

Fig.  187  (6). 

To  find  the  reactions  (beam  treated  as  a  whole) : 

0  =  RL  X  16  -  800  X  9  (point  of  moments  at  RR 
+  450  jf  =  RL  (clockwise  means  upward) 

0  =  800  x  7  +  RR  x  16  (point  of  moments  at 
-350#  =  RR  (counter  clockwise  means  upward) 
0  =  +450  -  800  +  350  =  check. 


188 


PART   III  — THE   DESIGN  OF  DETAILS 


To  find  the  shear: 

-50#  =  450  -  500  =  shear  for  a  section  midway  between 

the  supports. 
To  find  the  bending  moment: 
+2,350#ft.  =  450  x  8  -  500  x  2.5  =  MB  midway  between  the  supports. 

SECOND    PROBLEM CANTILEVER    BEAM 


\   2 

RL~2000 

Fig.  188  (a). 


e 

400  =  fl 


To  find  the 
0  = 

+2,000#  = 
0  = 

+400#  = 
0  = 

To  find  the 
+800#  = 

+400#  = 

To  find  the 
-3,600#ft.  = 
-l,600#ft.  = 


reactions  (beam  treated  as  a  whole)  : 

-1600  X  10  +  RL  X  8  (point  of  moments  at  RR) 

RL  (clockwise  means  upward)  __^__^ 

-1600  X  2  +  RR  X  8  (point  of  moments  at  RL)      »«.£V  4 

RR  (clockwise  means  downward) 

-1600  +  2000  -  400  =  check. 

shear: 

-1200  +  2000  =  shear  for  a  section  just  to  the 

right  of  RL- 
-1600  +  2000  =  shear  for  a  section  midway  be- 

tween RL  and  RR. 
bending  moment: 
-1200  x  3  =  MB  at  RL 
-1600  x  6  +  2000  x  4  =  MB  midway  between  RL  and  RR. 


1.  Combined  Loads.  —  Every  beam  must  support  the  uniformly  dis- 
tributed load  due  to  the  weight  of  the  beam  itself.  Besides  this  it  may 
support  an  additional  uniformly  distributed  load,  a  system  of  concen- 
trated loads,  or  both.  All  uniformly  distributed  loads  may  be  combined 
before  the  shear  or  bending  moment  is  computed,  but  it  is  usually  better 
to  treat  the  concentrated  load  systems  separately.  This  is  especially 
true  when  the  concentrated  loads  are  variable  or  movable,  or  when  the 
short-cut  method  of  the  following  paragraph  can  be  used  to  advantage. 
The  total  shear  for  any  section  is  the  sum  of  the  shear  due  to  the  uni- 
formly distributed  load  and  the  shear  due  to  the  concentrated  loads.  The 


total  bending  moment  at  any  point  is  the  sum  of  the  bending  moment  due 
to  the  uniformly  distributed  load  and  the  bending  moment  due  to  the 
concentrated  loads.  Shears  should  only  be  combined  when  they  are 
for  the  same  section.  Bending  moments  should,  as  a  rule,  be  combined 
only  when  they  occur  at  the  same  point  (compare  page  192  :  2) .  Whether 
the  shear  or  bending  moment  is  to  be  found  for  all  or  for  only  part  of  the 
loads  on  a  beam  it -is  important  that  the  reactions  used  correspond  to  the 
loads  under  consideration. 

2.  Short-Cut  Rule.  —  It  seems  desirable  to  introduce  one  "  short-cut  " 
method  for  finding  the  bending  moment  at  any  point  in  a  simple  beam 
(page  83  :  1)  under  a  uniformly  distributed  load  which  extends  the  full 
distance  between  the  two  supports.  This  form  of  loading  occurs  so  fre- 
quently in  practice  that  the  use  of  such  a  method  is  justified.  It  should 
be  used,  however,  only  by  those  who  have  thoroughly  mastered  the  more 
general  method  and  who  can  readily  derive  the  rule  for  themselves; 
otherwise  the  rule  is  likely  to  be  misused  with  regret.  The  rule  is  as 
follows:  The  bending  moment  at  any  point  of 

a  simple  beam  with  a  full  length  load  uniformly     a* /ft. 

distributed  is  equal  to  one-half  the  unit  load 
multiplied  by  the  product  of  the  segments.  It  is 
important  to  realize  that  this  method  is  not  Fig.  188  (6). 

general,  but  that  it  is  limited  to  a  beam  with 

a  full  load  uniformly  distributed  between  the  supports  with  no  load  extend- 
ing beyond  either  support.  It  does  not  therefore  apply  to  concentrated 
loads,  to  partial  uniform  loads,  or  to  cantilever  beams.  The  unit  load  is 
usually  in  pounds  per  linear  foot,  and  the  lengths  of  the  segments  cut  by 
the  point  of  moments  are  usually  in  feet;  the  resulting  bending  moment 
is  thus  in  pound-feet.  To  prove  the  rule  let  us  consider  a  simple  beam  of 
length  L  feet,  with  a  load  of  U  pounds  per  foot,  as  shown  in  Fig.  188  (6) .  Let 
it  be  desired  to  find  the  bending  moment  at  a  point  which  is  7  feet  from 
RL.  The  reactions  may  be  found  in  the  regular  way,  but  it  is  obvious 
that  for  symmetrical  loads  each  reaction  is  equal  to  one-half  the  total 

load,  or  in  this  case    -^— .     The  equivalent  concentrated  load  acting  at 

the  center  of  the  7  segment  is  U  Y.  The  bending  moment  is  found  in 
the  usual  way  as  follows: 


RL       Y 

L-  Y            ff 

L 

CHAPTER  XXX 


SHEAR  AND  BENDING  MOMENT 


189 


UL     v      _v      Y 

--x  Y  -  UY  x  - 


or 


UL_     UY 


Y(L  -  F).* 


1.  Relation  Between  Shear  and  Bending  Moment  —  Concentrated 
Loads,  f  —  When  the  bending  moment  is  required  at  several  different 
points  of  a  beam  it  is  sometimes  convenient  to  obtain  one  moment  from 
another.  Forjixed  concentrated  loads  the  bending  moment  under  any  load 
is  equal  to  the  bending  moment  under  an  adjacent  load  plus  the  product  of 
the  shear  for  a  section  between  the  loads  multiplied  by  the  distance  between 

the  loads.  Care  must  be  taken  in  combining 
moments  to  use  the  correct  signs;  the  signs  of 
the  additional  products  are  not  necessarily  the 
same  as  the  signs  of  the  shears.  From  one 
end  of  a  beam  to  the  other  the  bending 
moments  will  increase  as  long  as  the  shears 
bear  the  same  sign,  but  they  will  decrease 
when  the  shears  bear  the  opposite  sign.  This 
is  illustrated  in  the  design  of  pins,  page  280  :  3. 
The  rule  stated  above  will  now  be  proved.  In  Fig.  189  three  different 
forces  A,  B,  and  C  are  spaced  at  unequal  intervals  of  K,  M,  and  N,  caus- 
ing a  reaction  R  at  the  left-hand  support.  The  following  bending  moments 
may  be  obtained  in  the  usual  manner: 


Fig.  189. 


Atfl,     0 
At  A,  +RK 
AtB>+R(K 


-AM,     or     RK  +  (R  -  A)M 


For  the  maximum  moment  at  the  center,  Y  =  L  -  Y 


-,  hence  Afg=i 

m 


This  will  be  found  to  be  even  simpler  in  application  than  the  common  handbook 

VL*  WL 

formulas  MB  =  —  ,  MB  =  — ,  or  equivalent  expressions,  because  smaller  quantities 
o  5 

are  involved.    The  above  expression  is  given  for  the  sake  of  comparison,  but  it  should 
not  be  used  as  a  formula;  it  is  better  to  use  the  rule  because  that  applies  to  the  moment 

any  other  point  in  the  beam  as  well  as  at  the  center. 

f  For  uniformly  distributed  loads  see  page  244  :  3. 


AtC,  +R(K  +  M+  N)  -A(M+  N)  -BN,     or     RK  +  (R-  A)M  + 
(R  -A  -  B)N 

For  any  section  between  R  and  A  the  shear  is  R, 

A    "    B    "       "      "  R  -A, 
B    "    C    "       "      "  R  -A  -B 


it  If 

11  II 


It  is  evident  that  the  bending  moment  at  A  is  equal  to  the  moment  at 
R  plus  the  shear  for  a  section  between  R  and  A  multiplied  by  K.  Simi- 
larly, the  bending  moment  at  the  point  C  is  equal  to  the  bending  moment 
at  point  B  plus  the  shear  for  a  section  between  B  and  C  multiplied  by  N. 
This  may  be  found  to  apply  to  either  simple  or  cantilever  beams  for  any 
number  of  loads  and  for  any  spacing. 

2.  Live  Loads.  —  Not  all  loads  are  fixed  in  position  or  in  magnitude. 
The  loads  which  may  be  placed  temporarily  on  beams  or  girders  and 
which  may  be  changed  in  position  are  termed  "  live  loads  "  or  "  moving 
loads  "  to  distinguish  them  from  "  dead  loads  "  or  "  static  loads  "  which 
remain  in  one  position.     The  live  loads  are  usually  superimposed,  as 
trains,  trucks,  people,  water,  etc.;    the  dead  loads  include  the  weights 
of  the  beams  together  with  any  other  dead  loads  such  as  tracks,  floors, 
tanks,  etc.     When  the  live  loads  are  placed  in  a  certain  position  and 
stopped  they  become  static  loads,  and  shears  and  bending  moments  may 
be  found  in  the  same  manner  as  for  quiescent  loads.    Beams  which  are 
to  support  live  loads  must  be  designed  to  support  them  in  every  possible 
position,  and  accordingly  it  is  necessary  to  place  them  where  they  will 
have  the  greatest  effect.    The  effects  of  different  types  of  loads  in  differ- 
ent positions  are  analyzed  in  the  following  paragraphs.     When  these 
live  loads  are  applied  suddenly  the  shears  and  bending  moments   are 
greater  than  when  the  loads  are  stationary.    Provision  is  made  for  this 
"  impact "  by  adding  a  certain  percentage  of  the  live  load  according  to 
specifications.     Impact  will  not  be  considered   further  in  this  chapter, 
but  use  is  made  of  an  impact  formula  in  the  illustrative   problem   on 
page  225  : 1. 

3.  Live-Load    Shear  — -  Simple    Beams.  —  For    a    given   section  in  a 
simple  beam,  the  maximum  shear  will  usually  occur  when  the  longer  seg- 
ment is  fully  loaded  and  the  shorter  segment  is  unloaded.    In  Fig.  190  (a)  is 
shown  the  position  of  a  uniformly  distributed  load  which  will  cause  the 


190 


PART  III  — THE   DESIGN   OF  DETAILS 


Fig.  190  (a). 


maximum  shear  for  a  section  at  the  left  end  of  the  load.  This  shear  is 
equal  to  the  reaction  at  the  end  of  the  unloaded  segment  because 
there  are  no  intervening  loads  to  be  added  algebraically.  Note  that  a 
new  reaction  must  be  calculated  for  each  different  position  of  the  load. 
If  the  load  in  the  figure  were  moved  back  to  the  right,  the  left  reaction, 
and  therefore  the  shear,  would  be  reduced.  If  the  load  were  advanced 

past  the  section  on  to  the  shorter  segment 

£  JjTJ    the  left  reaction  would  be  increased  but  the 

shear  at  the  section  would  be  reduced  because 
the  additional  load  on  the  shorter  segment 
would  have  to  be  subtracted  from  the  reaction,  and  the  reaction  would  be 
increased  by  only  a  fraction  of  this  additional  load.  This  analysis  proves 
that  the  maximum  shear  for  any  section  will  occur  when  the  load  extends 
throughout  the  longer  segment  only.  Similarly,  a  single  concentrated  load 
to  cause  the  maximum  shear  for  any  section  should  be  placed  infinitely 
close  to  the  section  with  the  load  considered  to  be  entirely  upon  the  longer 
segment.  The  larger  of  two  concentrated  loads  should  be  placed  the  same 
as  a  single  load,  with  the  second  load  as  close  to  it  as  possible  but  on  the 
longer  segment,  as  in  Fig.  190  (6).  Three  or  more  concentrated  loads  are 
placed  in  the  same  manner  unless  one  or  more  of  the  end  loads  are  con- 
siderably smaller  than  the  intermediate  loads.  In  this  case  the  maximum 
shear  may  occur  when  the  first  heavy  wheel  is  placed 
adjacent  to  the  section  with  the  smaller  wheel  on  the  n 
shorter  segment,  as  in  Fig.  194.  This  is  illustrated  by  jrjg  190  (&). 

Cooper's  engine  loads,  page  193  :  1  .    The  absolute  maxi- 
mum shear,  or  the  maximum  of  maxima,  for  a  simple  beam  is  for  a  section 
taken  infinitely  close  to  the  reaction  so  that  the  shear  is  equal  to  the 
maximum  reaction. 

1.  Live-Load  Shear  —  Cantilever  Beams.  —  The  maximum  shear  on 
a  beam  which  is  supported  at  one  end  only  will  be  for  a  section  taken  at 
the  support  when  the  full  load  is  on  the  beam  (regardless  of  position). 
Similarly,  the  maximum  negative  shear  for  a  cantilever  beam  which 
overhangs  one  or  both  supports  will  be  for  a  section  taken  just  outside 
the  reaction  when  the  full  load  is  on  the  overhanging  portion;  this  shear 
is  not  affected  by  any  load  between  the  reactions.  The  maximum  posi- 
tive shear  for  the  same  beam  will  be  for  a  section  just  inside  the  reaction 


when  the  portion  of  the  beam  which   extends   outside  of   that  reaction 

and  the  portion  between  the  reactions  are  both  loaded,  as  in  Fig.  190  (c) ; 

there  should  be  no  load  on  any  portion  of  the 

beam  which  may  extend  beyond  the  other  re-  |j?~ 

action.      This   may    be   easily    proved.      For  pig.  190  (c). 

typical  shear  diagrams,  see  Fig.  193. 

2.  Live-Load  Bending  Moment  —  Simple  Beams.  —  Uniformly  Dis- 
tributed Loads.  The  maximum  bending  moment  at  any  point  B  feet 
from  the  left  end  of  a  simple  beam  L  feet  long  for  a  live  load  of  U  pounds 
per  foot  uniformly  distributed  over  a  distance  C  feet  will  occur  when  the 

ryri 

end  of  the  load  is  a  distance  X  =  B  -  -j-  from  the  left  end  of  the  beam. 

The  bending  moment  at  this  point  will  increase  as  the  distance  C  increases; 

it  is  greatest  when  the  load  extends  the  full 
length  L.  The  absolute  maximum  will  occur 
at  the  center  of  the  beam  under  a  full  load. 
These  statements  will  now  be  proved  in  the 
Fig.  190  (d).  order  given.  Referring  to  Fig.  190  (d),  we  car 

find  the  following  values  in  the  usual  manner 


rjrt  IT        v- 
u(_/  I  Li  —  A  — ^ 


=  MB  at  a  distance  B  from  RL 


B 


_  U(B  -X) 


^— 


This  may  be  reduced  to  this  form: 

r        BC*    B*    /      BC\        xn 

J[BC  -  2L  -^  +  (B  •  T)X-  TJ 
The  value  of  X  which  will  produce  the  maximum  bending  moment  ma? 
be  found  by  differentiating  this  expression  with  respect  to  X,  and  placin; 
the  first  derivative  equal  to  zero,  thus: 

=  0,        whence         X  -- 

If  we  substitute  this  value  of  X  in  the  last  expression  for  bending  mo 
ment  we  have: 


CHAPTER  XXX 


SHEAR  AND  BENDING  MOMENT 


191 


V 


BC*    &    /      scy     (B-  L) 

LBC  -  2L  -  ~2  +  (B  -  T) 2~~  J 


which  may  be  reduced  to  this  form: 


The  value  of  C  which  will  produce  the  maximum  bending  moment  .may 
be  found  by  differentiating  this  expression  with  respect  to  C,  and  placing 
the  first  derivative  equal  to  zero,  thus: 


(l  -  f)  f1  -  J)  =  °.      whence      C  -  L. 


UB 


If  we  substitute  this  value  of  C  in  the  last  expression  for  bending  moment 
we  have: 

UB  (l  -  |)  (L  -  ^),         or        -^  (#-?)•    (Compare  page  188:  2.) 

The  value  of  B  which  will  produce  the  maximum  bending  moment  may 
be  found  by  differentiating  this  expression  with  respect  to  B,  and  placing 
the  first  derivative  equal  to  zero,  thus: 


UL  L      2B\ 
~~2~  \     "  ~LJ  =    '        whence 


2' 


1.  Live-Load  Bending  Moment  —  Simple  Beams.  —  Concentrated 
Loads.  The  maximum  bending  moment  at  any  point  of  a  simple  beam  for 
a  system  of  moving  concentrated  loads  will  occur  when  one  of  the  concen- 
trated loads  is  at  that  point.  The  maximum  bending  moment  due  to  two 
loads  will  occur  when  the  larger  load  is  placed  at  the  given  point  with  the 
other  load  on  the  longer  segment  as  near  the  first  load  as  possible.  The 
placement  of  more  than  two  loads  to  give  the  maximum  bending  mo- 
ment is  not  so  simple.  Often  two  or  three  different  loads  in  turn  must  be 
placed  at  the  point,  and  the  corresponding  bending  moments  must  be 
computed  and  compared.  The  following  criterion  must  be  satisfied  by 
the  critical  load  which  is  placed  at  the  given  point:  the  average  load  on 
segment  should  be  greater  than  the  average  load  on  the  whole  beam  when 


the  critical  load  is  considered  on  that  segment,  but  less  when  it  is  considered 
on  the  other  segment*  The  average  load  is  the  sum  of  the  loads  on  a 
segment,  or  whole  beam,  divided  by  the  corresponding  length.  Often 
more  than  one  load  will  satisfy  this  criterion.  It  is  sometimes  possible 
to  tell  by  inspection  that  one  of  two  wheels  is  the  critical  wheel;  in  this 
case  it  is  unnecessary  to  apply  the  criterion.  The  greatest  bending  mo- 
ment that  can  occur  on  a  simple  beam  for  a  series  of  moving  concen- 
trated loads  will  be  found  near  the  center  of  the  beam,  but  not  as  a  rule 
at  the  center.  The  absolute  maximum  bending  moment,  or  maximum  of 
maxima,  will  occur  under  one  of  the  concentrated  loads  when  the  center  of 
the  beam  is  midway  between  that  load  and  the  center  of  gravity  of  all  the 
loads  on  the  beam.  The  critical  load  is  always  one  of  the  two  loads  ad- 
jacent to  this  center  of  gravity,  usually  the  nearest  load.  The  relative 
position  of  the  center  of  gravity  will  often  change  when  the  loads  are 
moved,  because  one  or  more  loads  may  come 
on  one  end  of  the  beam  while  others  may  ^  -  2  -  . 
move  off  the  other  end.  Enough  trials  must 
be  made  to  make  sure  that  the  bending  mo- 
ment under  one  load  is  greater  than  under 
either  adjacent  load  when  each  is  placed  for 
the  maximum.  For  special  suggestions  for 
placing  the  concentrated  wheel  loads  of  Cooper's 

conventional  locomotives,  see  page  195  :  1.  To  prove  that  the  maximum 
bending  moment  on  a  simple  beam  will  occur  when  the  critical  load  P 
(Fig.  191)  is  placed  as  far  on  one  side  of  the  center  of  the  beam  as  the 
center  of  gravity  of  all  the  loads  on  the  beam  is  on  the  other  side,  let  Y 
represent  the  distance  from  P  to  the  center  of  gravity  of  11  the  loads  Q, 
X  the  distance  from  P  to  the  center  of  gravity  of  all  the  loads  N  on  the 
left  segment,  and  B  the  distance  from  P  to  the  reaction  RL,.  Then 


o 

O    O 

n  o  o 

RL 
B 

.  x  , 

Y 

"»' 
L                       , 

Fig.  191. 


Q(L  -  B  -  Y)  Q(L  -  B  -  Y)B 

—j—      -  =  RL,  and   -         -^—        --  NX  =  the  bending  moment 
L/  Lt 

under  the  load  P.  The  value  of  B  which  will  produce  the  maximum 
bending  moment  may  be  found  by  differentiating  this  expression  with 
respect  to  B,  and  placing  the  first  derivative  equal  to  zero,  thus: 

*  For  derivation  see  Marburg's  "Framed  Structures  and  Girders,"  Part  I,  McGraw- 
Hill  Book  Co.,  Inc.,  New  York. 


192 


PART  III  — THE   DESIGN   OF  DETAILS 


whence 


or 


1.  Illustrative  Problem  —  Two  Concentrated  Live  Loads.  —  (See  page 
195  :  1  for  more  than  two  loads.) 

To  find  the  maximum  bending  moment  on  a  20-foot  beam  due  to  two 
concentrated  live  loads  of  8000#  and  6000#  respectively,  spaced  7  feet 
nooo  6000  ,  apart.  The  distance  from  the  larger  load  to 
-  &  -  Q  —  7-  —  Q  4J  .  the  center  of  gravity  may  be  found  by  mo- 


Fie  192  (a)  '    ments>  taking  the  point  of  moments  under  the 

larger  load.    The  sum  of  the  moments  of  the 

loads  taken  separately  must  equal  the  moment  of  the  sum  of  the  loads 
(i.e.,  the  resultant),  thus:  6000  x  7  =  (6000  +  8000)  X,  whence  X  =  3  feet. 
The  8000  load  should  be  placed  1J  feet  from  the  center  of  the  beam,  as 
shown  in  Fig.  192  (a) .  The  reaction  may  be  found  either  from  the  original 
two  loads  or  from  the  resultant  thus: 


or 


5950#  =  (8000  X  11£  +  6000  X  4|)n-  20  =  RL 
5950#  =  14,000  x  8$  -s-  20  =  RL 


The   maximum   bending   moment   under   the   larger   load   is   50,580#ft. 
=  5950  x  8J. 

2.  Bending  Moment  —  Simple  Beams.  —  Combined  Loads.  Con- 
centrated loads  exist  only  in  conjunction  with  uniformly  distributed 
loads.  The  latter  may  be  due  simply  to  the  weight  of  the  beam  itself, 
or  to  track  or  floor  loads  as  well.  The  maxi- 
mum bending  moment  for  the  uniformly 
distributed  load-  is  at  the  center,  but  the 
maximum  for  moving  concentrated  loads  is 
usually  at  another  point.  The  maximum  for 
the  combined  loads  will  not  be  found  at  either 
of  these  points  but  somewhere  between  them. 
This  may  be  shown  graphically  by  plotting 
the  moment  diagram  for  the  uniformly  distributed  load  above  a  base 
line  and  that  for  the  concentration  loads  below  the  line,  as  in  Fig.  192  (b). 
The  longest  ordinate  m  from  one  curve  to  the  other  represents  the  maxi- 
mum total  bending  moment.  The  position  of  this  point  of  moments  is 


Fig.  192  (6). 


in  the  section  for  which  the  shear  is  zero;  this  may  be  found  either  alge- 
braically or  graphically.  However,  it  is  seldom  necessary  to  locate  this 
point  because  at  least  one  of  the  moment  curves  is  nearly  horizontal 
between  the  two  points  of  maximum  bending  moments.  It  is  customary 
to  combine  the  maximum  bending  moment  due  to  moving  concentrated 
loads  with  the  maximum  due  to  uniformly  distributed  loads,  although 
they  do  not  occur  at  the  same  point.  The  slight  error  is  on  the  side  of 
safety.  The  maximum  bending  moments  due  to  fixed  concentrated  loads 
and  uniformly  distributed  loads  should  not  be  combined  unless  they  occur 
at  points  so  close  together  that  the  excess  will  not  be  too  great. 

3.  Live-Load    Bending    Moment  —  Cantilever    Beams.  —  The    maxi- 
mum bending  moment  for  a  beam  supported  at  one  end  only  will  occur 
at  the  edge  of  the  support  when  the  loads  are  placed  as  far  from  the  sup- 
port as  possible.    For  beams  which  overhang  one  or  both  of  two  supports 
there  will  be  a  maximum  positive  and  a  maximum  negative  bending 
moment.    One  will  be  found  at  one  of  the  supports  when  the  overhang- 
ing end  is  fully  loaded,  the  loads  being  placed  as  far  from  the  support 
as  possible    The  other  maximum  for  fixed  loads  will  occur  at  that  sec- 
tion between  the  supports  for  which  the  total  shear  is  zero;  the  maximum 
for  live  loads  will  occur  midway  between  the  supports  when  only  the 
portion  of  the  beam  between  the  supports  is  loaded,  the  cantilever  end 
being  empty.    The  point  of  contraflexure  is  the  point  at  which  the  bend- 
ing moment  is  zero.    Typical  shear  and  moment  diagrams  are  shown  in 
Fig.  193.      Positive  bending  moments  have  been  plotted   downward  !to 
represent  more  nearly  the  direction  in  which  the  beams  bend. 

4.  Restrained    beams   and   continuous   beams   are   not   treated   here 
because  the  structural  draftsman  is  seldom  called  upon  to  design  them. 
Beams  and  girders  with  end  connection  angles  are  in  a  measure  restrained 
or  "  fixed  "  at  the  ends.     The  amount  of  restraint  depends  so  largely 
upon  the  efficiency  of  rivets  in  tension  and  upon  the  rigidity  of  the  sup- 
porting members  that  it  is  customary  to  design  such  beams  as  simple 
beams.     Even    beams  which  are  inserted  into   masonry  walls   are  not 
always  sufficiently  imbedded  to  insure  a  fixed  condition,  except  such 
beams  as  lintels,  which  support  masonry  walls  over  openings.    It  is  safer 
to  design  these  beams  as  simple  beams  than  to  place  so  much  dependence 
upon  the  masons.      Office-building  beams  are  often  so  braced  to  the 


CHAPTER  XXX 


SHEAR  AND  BENDING  MOMENT 


193 


columns  that  they  must  be  designed  as  fixed  beams,  but  these  and  similar 
beams  are  usually  designed  in  the  Designing  Department  and  therefore 
are  beyond  the  scope  of  this  book.*  Beams  which  have  more  than  two 
supports  are  statically  indeterminate.  Their  use  is  not  recommended 
ordinarily.  If  desired  these  continuous  beams  may  be  designed  by  the 


^Moment  Diagram , 


Shear  Diagram 


.  ShdZr  Diagra: 

Fig.  193. 


5/!sar  Diagram 


"  Theorem  of  Three  Moments"  *,  but  the  lighter  beams  (such  as  purlins) 
which  extend  over  three  supports  primarily  to  give  rigidity  to  a  structure 
are  more  often  designed  as  simple  beams. 

1.  Conventional  Wheel-Load  Systems.  —  The  floor  systems  (beams, 
stringers  and  floor  beams)  and  the  main  girders  of  railroad  bridges  are 
usually  designed  to  support  a  specified  live  load  of  two  freight  locomo- 
tives with  concentrated  wheel  loads  followed  by  a  uniformly  distributed 
train  load.  For  very  short  spans  an  alternate  loading  of  the  two  driving, 
axles  of  a  passenger  locomotive  is  specified.  Formerly  almost  every 
railroad  specified  a  different  locomotive  until  Theodore  Cooper  proposed 
his  system  of  conventional  engine  loads  for  the  sake  of  uniformity.  He 
classified  his  engines  according  to  the  axle  loads,  the  spacing  between 
loads  being  the  same  for  all  engines.  As  the  specified  axle  loads  have 
increased  considerably  since  his  system  was  adopted,  the  spacing  between 

*  See  Kirkham's  "Structural  Engineering,"  McGraw-Hill  Book  Co.,  Inc.,  New 
York;  Fuller  and  Johnston's  "Strength  of  Materials,"  John  Wiley  and  Sons,  Inc., 
New  York,  and  others. 


loads  is  less  than  for  actual  locomotives.  The  difference  in  results  is  on 
the  side  of  safety  (except  for  cantilever  bridges  and  turntables)  and  Cooper's 
Loadings  are  quite  generally  specified.  The  engines  are  classified  ac- 
cording to  the  axle  loads  on  the  driving  wheels,  and  all  other  axle  loads 
vary  proportionately.  The  axle  loads  on  the  drivers  of  an  "  E60  "  load- 
ing are  each  60,000  pounds,  and  the  train  is  6000  pounds  per  linear  foot 
of  track.  Similarly,  the  corresponding  loads  of  an  "  E40  "  loading  are 
40,000  and  4000,  and  the  shears  and  bending  moments  for  E40  are  four- 
sixths  (two-thirds)  of  the  corresponding  shears  and  bending  moments 
for  E60.  This  relation  makes  it  possible  to  prepare  a  table  of  shears 
and  moments  for  one  class  of  loading  and  to  use  this  table  in  getting  shears 
and  bending  moments  not  only  for  that  class  but,  by  proportion,  for 
other  classes  as  well.  Such  a  table  |  is  given  on  page  318.  E60  loading 
is  chosen  in  accord  with  the  more  recent  specifications  of  the  leading  rail- 
road companies.  In  the  table  the  axle  loads  per  track  have  been  divided 
by  two  to  give  the  wheel  loads  per  rail,  and  all  shears  and  moments  result 
accordingly.  This  usually  corresponds  to  the  loads  supported  by  one 
stringer  or  girder.  When  two  stringers  are  used  under  each  rail  these 
values  must  be  subdivided  again.  Shears  and  moments  are  taken  as 
if  the  loads  were  applied  directly  to  the  stringers  or  girders,  although 
as  a  matter  of  fact  the  loads  are  transmitted  to  them  through  the  track 
(i.e.,  the  rails  and  the  ties).  The  distances  between  wheels  have  been 

1" 
plotted  in  the  table  to  a  scale  of  ^  =  1'.    The  number  of  wheels  which 

may  come  on  a  given  span  may  best  be  determined  by  plotting  the  length 
of  the  span  along  the  edge  of  a  strip  of  paper  to  this  scale  and  then  sliding 
the  strip  along  the  diagram.  The  significance  of  the  different  values 
is  explained  in  the  table.  Students  should  verify  enough  values  for 
shears,  moments,  and  positions  of  centers  of  gravity  to  enable  them  to 
understand  their  full  meaning.  The  use  of  the  table  is  illustrated  by  the 
solution  of  the  typical  problems  which  follow. 

2.  Maximum  Shear  on  Beam  —  Cooper's  Loading.  — •  The  loading 
which  will  cause  the  maximum  shear  on  a  simple  beam  depends  upon 

t  Numerical  values  for  shears,  bending  moments,  floor-beam  reactions,  etc.,  are 
tabulated  in  Ketchum's  "Structural  Engineers'  Handbook,"  McGraw-Hill  Book  Co., 
Inc.,  New  York. 


194 


PART  III  — THE   DESIGN  OF  DETAILS 


the  span.  For  spans  up  to  12.5  feet  the  special  loading  of  two  37,500# 
wheel  loads  7  feet  apart  should  be  used.  For  longer  spans  (except  those 
between  23.0  and  27.3  feet)  the  maximum  shear  on  the  beam  will  equal 
the  left  reaction  (when  the  engines  face  toward  the  left  as  in  the  diagram) 
when  the  first  driver  (wheel  2)  is  placed  at  the  left  end.  For  spans  be- 
tween 23.0  and  27.3  the  maximum  shear  on  the  beam  will  equal  the  right 
reaction  when  wheel  5  is  placed  at  the  right  end.  This  is  due  to  the  effect 
of  wheel  1,  which  in  this  case  is  on  the  beam. 

Illustrative  Problem  —  General  Case.  —  To  find  the  maximum  shear 
on  a  74-foot  deck  girder  for  Cooper's  EGO  loading.  The  figures  printed 
along  the  vertical  line  under  wheel  2  give  the  distances  from  that  wheel 
to  the  wheel  over  the  corresponding  vertical  of  the  zigzag  line.  The 
distance  to  wheel  14  is  found  to  be  71  feet,  and  thus  with  wheel  2  at  the 
left  end,  wheel  14  is  3  feet  =  74  —  71  from  the  right  end.  The  moment 
of  these  loads  about  RR  is  equal  to  the  moment  about  wheel  14  plus  the 
product  of  the  sum  of  the  loads  by  the  additional  lever  arm.  (This  may 
be  proved  as  on  page  189  : 1.)  The  moment  of  wheels  2-14  about  wheel 
14  is  found  by  following  down  the  vertical  line  under  wheel  14  to  the 
heavy  vertical  line  in  the  moment  table,  then  toward  the  left  to 
the  number  just  to  the  right  of  the  line  through  wheel  2,  viz.: 
11,900  thousand  pound-feet.  The  sum  of  loads  2-14  is  found  simi- 
larly in  the  shear  table  to  be  333  thousand  pounds.  The  total  moment  is 
then  12,900  =  11,900  +  333  x  3  in  thousands  of  pound-feet.  The  maxi- 
mum shear  is  equal  to  the  reaction  RL  which  is  this  total  moment  divided 
by  the  span,  or  174  thousand  pounds  =  12,900  -f-  74. 

Illustrative  Problem  —  Special  Case.  —  To  find  the  maximum  shear  on 
a  24-foot  stringer  for  Cooper's  EGO  loading.  If  wheel  2  were  placed  at 
the  left  end,  wheel  6  would  be  at  RR  and  only  the  four  drivers  would  be 
on  the  span.  (The  distance  24  feet  from  wheel  2  to  wheel  6  is  not  dupli- 
cated in  the  table  because  it  is  the  same  as  from  wheel  11  to  wheel  15.) 
For  beams  between  23.0  and  27.3  feet  long  the  maximum  shear  will  equal 
the  right  reaction  RR  when  wheel  5  (or  14)  is  placed  there,  since  not  only 
the  four  drivers  but  the  pilot  wheel  1  (or  10)  comes  on  the  span.  The 
parts  of  the  shear  and  moment  tables  at  the  right  of  the  zigzag  line  should 
be  used  in  much  the  same  way  as  the  parts  at  the  left.  Thus,  the  dis- 
tance from  wheel  10  to  wheel  14  is  found  to  h"  23,  the  sum  of  the  loads 


135,  and  the  moment    1860.     Hence,  the   maximum   shear  =  RR  =  83 
=  (1860  +  135  X  1)  -f-  24  in  thousands  of  pounds. 

1.  Maximum  Shear  for  Any  Section  —  Cooper's  Loading.  —  The 
loading  which  will  cause  the  maximum  shear  for  any  section  of  a  simple 
beam  depends  upon  the  relative  lengths  of  the  segments.  When  the 
longer  segment  does  not  exceed  12.5  feet  the  special  loading  of  two  37,500# 
wheel  loads  should  be  used.  When  the  longer  segment  is  between  23.0 
and  27.3  feet  and  the  shorter  segment  not  over  9  feet,  the  maximum  shear 
for  the  section  will  be  found  when  wheels  1  to  5  are  on  the  longer  segment 
with  wheel  5  next  to  the  section,  no  load  being  on  the  shorter  segment. 
For  all  beams  over  34.5  feet  long  the  maximum  shear  for  any  section 
will  be  found  when  the  longer  segment  is  fully  loaded  and  wheel  2  is  next 
to  the  section  (wheel  1  being  on  the  shorter  segment  if  the  latter  is 
more  than  8  feet  long).  See  Fig.  194.  For  all  other  spans  the  maximum 
shear  for  any  section  will  be  found  when  the 
longer  segment  is  fully  loaded  and  when  r— 

\RL 


n     DODO      o  n 


either  wheel  2  or  the  first  wheel  of  the  special  F- 

loading    is   next   to  the  section,   depending 

upon  the  relative  lengths  of  the  segments.  .  The  shear  for  any  section  is 

not  necessarily  equal  to  the  reaction,  for  when  wheel  1  is  on  the  shorter 

segment  it  must  be  deducted. 

Illustrative  Problem.  —  To  find  the  maximum  shear  for  a  section  10 
feet  from  the  end  of  a  30-foot  stringer  for  Cooper's  E40  loading.  The 
effects  of  two  loadings  must  be  compared  because  the  beam  is  less  than 
34.5  feet  long.  Placing  wheel  2  (or  11)  next  to  the  section,  we  find  that 
wheel  5  (or  14)  is  5  feet  from  the  right  end.  The  left  reaction  due  tc 
this  position  of  wheels  1  to  5  is  64  =  (1250  +  135  X  5)  ^  30  for  E60. 
and  the  corresponding  shear  is  49  thousand  pounds  =  64  -  15.  Placing 
the  first  37,500#  wheel  of  the  special  loading  next  to  the  section, 
we  find  the  shear,  which  is  equal  to  the  reaction,  is  only  41  thou- 
sand =  37,500  (13  +  20)  -=-  30.  The  maximum  shear  for  E40  is  there- 
fore 33  =  49  X  f . 

2.  Maximum  Floor-Beam  Reaction  —  Cooper's  Loading.  —  In  design 
ing  a  through  railway  bridge  it  is  necessary  to  determine  the  maximun 
concentrations  on  the  floor  beams.  These  are  used  in  designing  the  floo: 
beams  and  the  girders  and  also  the  connections  of  the  stringers  to  th< 


CHAPTER  XXX 


SHEAR  AND  BENDING  MOMENT 


195 


?o_s 


floor  beams  and  the  floor  beams  to  the  girders.  The  concentration  on 
an  intermediate  floor  beam  at  each  stringer  point  is  equal  to  the  right- 
hand  reaction  of  one  stringer  plus  the  left-hand  reaction  of  the  adjacent 
stringer.  The  loads  should  be  placed  to  make  this  sum  a  maximum,  but 
they  cannot  be  placed  to  make  both  reactions  maximum  at  the  same  time 
lost  the  engines  overlap.  The  maximum  concentration  or  "  floor-beam 
reaction  "  will  be  found  when  one  of  the  inner  drivers  of  the  second 
engine  (wheel  12  or  13)  is  placed  directly  over  the  floor  beam.  It  is  usually 
necessary  to  try  both  wheel  12  and  wheel  13  over  the  floor  beam  in  order 
to  ascertain  which  will  give  the  larger  floor-beam  reaction.  A  criterion 
is  sometimes  used  to  determine  which  wheel  to  place  over  the  floor  beam. 
There  is  not  much  advantage  to  be  gained  by  its  use  because  both  wheels 
12  and  13  often  satisfy  the  criterion  and  both  must  be  tried  the  same  as 
if  no  criterion  were  used.  Care  should  be  taken  that  the  load  over  the 
floor  beam  is  considered  once,  but  only  once,  in  finding  the  floor-beam 
reaction.  It  may  be  included  in  the  right  reaction  of  the  left-hand  span, 
or  in  the  left  reaction  of  the  right-hand  span,  or 
^  may  ke  considered  independently. 

Illustrative  Problem.  —  To  find  the  maximum 
floor-beam  reaction  at  each  stringer  point  in  a 
bridge  with  15-foot  panels,  center  to  center  of 
floor  beams,  for  Cooper's  E60  loading.  Placing  wheel  12  over  the  floor 
beam,  as  in  Fig.  195  (a)  ;  the  reaction  at  this  floor  beam  may  be  found  from 
the  table  as  follows: 

22.0  =  (240  +  45  X  2)  -=-  15  =  RR 

30.0  =  (150  +  60  x  5)  -v-  15  =  RL 

30.0  =  load  at  floor  beam 

82  .  0  =  total  floor-beam  reaction  in  thousands  of  pounds. 

This  result  may  be  obtained  without  the  table  by  combining  the  lever 
arms  of  equal  loads  for  both  spans,  thus: 

82.0  =  [15.0  x  2  +  30.0(10  +  15  +  10  +  5)]  -=-  15. 

Similarly,  by  placing  wheel  13  over  the  floor  beam  another  value  is  ob- 
tained which  in  this  case  is  smaller  (81.3). 

1.   Absolute  Maximum  Bending  Moment  —  Cooper's  Loading.  —  The 
maximum  bending  moment  for  a  simple  beam  not  over  11.4  feet  long 


t 


c 


Fig  195  (a) 


will  occur  at  the  center  when  one  of  the  two  37,500#  wheel  loads  is  placed 
at  the  center.  For  any  simple  beam  or  girder  from  11.4  to  about  90  feet 
long  the  absolute  maximum  bending  moment  will  occur  under  one  of 
the  inner  drivers  of  the  second  engine  (wheel  12  or  13)  when  the  dis- 
tance between  this  driver  and  the  center  of  gravity  of  all  the  loads  on 
the  beam  is  bisected  by  the  center  of  the  beam  (page  191  : 1).  The 
critical  wheel  will  be  adjacent  to  the  center  of  gravity,  usually  the  wheel 
nearest  the  center  of  gravity.  The  first  engine  will  have  an  equal  effect 
for  spans  up  to  about  50  feet,  but  never  a  greater  effect.  For  girders 
longer  than  about  70  feet  a  portion  of  the  uniformly  distributed  train 
load  must  be  considered.  The  relative  position  of  the  center  of  gravity 
then  changes  with  every  movement  of  the  loads,  and  more  trials  are 
usually  needed  to  determine  the  proper  position  of  the  loads.  For  girders 
longer  than  about  90  feet  the  critical  wheel  should  be  determined  from 
the  criterion  (page  191  : 1). 

Illustrative  Problem.  —  To  find  the  maximum  bending  moment  on  a 
40-foot  girder  for  Cooper's  E50  loading.     By  plotting  the  length  to  a 

1" 
scale  of  r^  =  1'  (40  -=-  16  =  2£  inches)  on  the  edge  of  a  strip  of  paper  and 

sliding  it  along  under  the  wheels  in  the  table  to  include  different  com- 
binations of  wheels,  it  is  found  that  the  inner  drivers  12  and  13  are  brought 
in  the  vicinity  of  the  center  when  wheels 

10-16  are  on  the  girder.  The  position  of  (?  Q  p  D  D  On 
the  center  of  gravity  of  these  wheels  may  U^ 
be  found  from  the  corresponding  wheels  of 
the  first  engine  (wheels  1-7)  to  be  0.4  of  a 
foot  to  the  right  of  wheel  13.  The  critical  wheel  is  always  adjacent  to  the 
center  of  gravity,  and  for  spans  less  than  90  feet  it  is  one  of  the  inner 
drivers;  in  this  case,  therefore,  the  maximum  bending  moment  will  occur 
under  wheel  13  when  it  is  placed  0.2  foot  =  0.4  -=-  2  to  the  left  of  the 
center  of  the  span,  as  shown  in  Fig.  195  (6),  wheel  16  being  1.2  feet  from  the 
right  end.  For  E60  loading,  the  moment  of  all  wheels  about  wheel  16 
is  3230  thousand  pound-feet,  and  the  sum  of  the  loads  10-16  is 
174  thousand  pounds.  The  left  reaction  is  86  thousand  pounds 
=  (3230  +  174  X  1.2)  4-  40.  The  bending  moment  under  wheel  13  is 
980  thousand  pound-feet  =  86  X  19.8  -  720,  the  value  720  being  the 


ls'8 


20.2 


Fig.  195  (6). 


196 


PART  III  — THE   DESIGN   OF  DETAILS 


moment  of  wheels  10-13  taken  directly  from  the  moment  table.  The 
bending  moment  for  E50  loading  is  f  of  980  or  820  thousand  pound-feet. 
In  the  use  of  the  table,  consistent  accuracy  should  be  used. 

1.  Maximum  Bending  Moment  at  Any  Point  —  Cooper's  Loading. — 
The  maximum  bending  moment  at  any  point  of  a  beam  or  girder  will 
occur  when  the  critical  wheel  is  placed  at  that  point.     For  spans  up  to 
100  feet  the  critical  wheel  will  be  either  wheel  12  or  wheel   13,  although 
in  some  cases  the  maximum  moment  will  occur  when  the  engines  face 
the  longer  segment  instead  of  the  shorter.     For  spans  over  100  feet  the 
critical  wheel  *  should  be  found  from  the  criterion  on  page  191  : 1 . 

2.  Through  Girders  —  Cooper's  Loading.  —  The  live  loads  in  a  through 
bridge  are  applied  to  each  girder  in  the  form   of  concentrated  loads  at 
the  floor-beam  connections.    The  action  of  the  wheel  loads  may  be  best 
shown  by  sketching  the  stringers  as  if  they  rested  on  top  of  the  floor 


4    O   S    O       S     20       S       O  5 

a 

O  5 

13        14 

Os-O    s 

w       w 
•«O  s  O 

s     t 

Ruff 
Ties 
Stringers 
Floor  Beams 

..Girder 

1 

=^ 

I  —  !  

\ 

Fig.  196. 

beams,  and  the  floor  beams  as  if  they  rested  on  top  of  the  girders,  as  in 
Fig.  196,  although  in  reality  web  connections  are  used  and  the  trains 
pass  "  through  "  the  bridge  between  the  girders.  The  end  stringers  may 
rest  directly  upon  the  abutments  or  they  may  be  connected  to  end  floor 
beams;  in  either  case  the  effect  upon  the  girder  is  virtually  the  same, 
except  for  the  details  at  the  ends.  If  the  bridge  supports  a  single  straight 
track,  each  floor  beam  is  symmetrically  loaded  and  the  corresponding 
girder  load  (for  live  loads)  is  numerically  equal  to  the  floor-beam  reaction. 
The  maximum  floor-beam  reaction  cannot  occur  at  more  than  one  floor 

*  The  critical  wheels  for  different  segments  are  indicated  in  a  table  in  Ketchum's 
"  Structural  Engineers'  Handbook,"  McGraw-Hill  Book  Go.,  Inc.,  New  York. 


team  at  the  same  time,  and  it  is  necessary  to  so  place  the  loads  that  the 
bending  moment  at  the  floor  beam  nearest  the  center  of  the  girder  will 
be  a  maximum.  It  so  happens  that  the  bending'  moment  at  any  panel 
point  is  the  same  as  if  the  wheel  loads  were  applied  directly  to  the  top 
flange  of  the  girder,  and  hence,  the  position  of  the  loads  which  will  cause 
the  maximum  bending  moment  at  any  floor  beam  is  found  as  in  the  pre- 
ceding paragraph.  The  bending  moment  at  this  point  may  be  found  as 
in  a  deck  girder  or  else  from  total  concentrated  loads  obtained  by  com- 
bining the  different  floor-beam  reactions  with  the  corresponding  dead 
loads  (page  225  : 1).  The  maximum  shear  in  the  end  panel  will  occur 
when  the  loads  are  placed  to  give  a  maximum  bending  moment  at  the 
first  floor-beam  point. 

Illustrative  Problem.  —  To  find  the  maximum  bending  moment  on  a 
girder  of  a  through  railway  bridge  of  four  15-foot  panels  for  Cooper's 
EGO  loading.  The  maximum  bending  moment  will  occur  at  the  center 
floor  beam  when  the  critical  wheel  (either  12  or  13)  is  placed  at  that 
point.  Let  us  assume  that  wheel  12  is  the  critical  wheel  |  and  that  the 
loads  are  placed  as  in  Fig.  196.  The  floor-beam  reaction  at  the  center 
floor  beam  is  82,000#  as  determined  on  page  194  :  2.  In  a  similar  manner 
the  corresponding  floor-beam  reactions  at  the  first  and  third  quarter 
points  are  found  to  be  39,900#  and  52,100#  respectively.  The  bending 
moment  for  these  loads  combined  with  impact  and  dead  loads  is  found 
on  page  225  : 1 ,  and  the  shear  on  page  250  : 3. 

3.  Trusses  —  Cooper's  Loading.  —  Trusses  may  be  designed  for 
Cooper's  loading  or  for  equivalent  uniformly  distributed  loads.  The 
table  on  page  318  may  be  used  to  advantage  in  finding  the  live-load 
stresses  in  trusses,  but  the  placement  of  the  loads  is  beyond  the  scope 
of  this  book. | 

t  Both  positions  should  be  tried  to  determine  which  causes  a  maximum.  In  this 
case  a  slightly  greater  bending  moment  is  found  when  wheel  13  is  placed  at  the  center, 
but  the  difference  is  so  small  it  is  disregarded  in  order  to  simplify  different  steps  in  a 
series  of  problems  based  upon  the  values  given  here. 

t  See  Marburg's  "Framed  Structures  and  Girders,"  Part  I,  McGraw-Hill  Booh 
Co.,  Inc.,  New  York. 


CHAPTER  XXXI 
THE  DESIGN  OF  BEAMS 

SYNOPSIS:  Beams  are  proportioned  according  to  the  bending  moment  and  shear 
determined  from  the  external  forces.  The  shape  and  the  size  of  the  cross  section 
are  designed  with  due  regard  to  bending,  shearing,  buckling,  bearing,  and  deflection. 

1.   General.  —  Most  structures  are  designed  in  a  Designing  Depart-     is  to  support  plastered  ceilings,  shafting,  or  machinery;   when  necessary, 


ment,  although  draftsmen  are  often  called  upon  to  design  beams.  Every 
draftsman  should  be  familiar  with  the  methods  of  design  if  for  no  other 
reason  than  to  design  the  connections  properly.  The  general  arrange- 
ment of  the  beams  in  a  structure  is  usually  determined  in  the  designing 
room.  Beams  which  support  machinery,  tracks,  runways,  walls,  etc., 
must  be  located  to  meet  the  given  conditions.  Beams  near  openings  in 
floors  or  walls  must  be  placed  in  the  proper  relation  to  these  openings. 
The  spacing  of  floor  beams  and  roof  beams  or  purlins  in  buildings  de- 
pends upon  the  type  of  flooring  or  roofing  and  upon  the  superimposed 
loads.  The  type  and  the  length  of  a  beam,  the  form  of  loading,  the  mag- 
nitude of  the  loads,  and  the  distance  between  beams  all  have  their  effect 
upon  the  shear  and  bending  moment,  as  explained  in  the  preceding 
chapter.  After  these  are  once  determined  the  design  of  the  beam,  or 
the  determination  of  the  proper  cross  section,  is  the  same  for  all,  regard- 
less of  the  sign  of  the  shear  or  the  bending  moment. 

2.  Points  Considered.  —  Beams  should  be  designed  to  give  proper 
resistance  to  bending,  shearing,  buckling,  and  deflection.  Beams  which 
rest  upon  other  beams  or  walls  must  have  sufficient  bearing  area  (page 
203  : 1).  Beams  are  usually  designed  first  to  resist  bending,  and  then  the 
resistance  of  the  resulting  beam  to  vertical  and  horizontal  shear  is  in- 
vestigated. Beams  seldom  buckle  except  under  a  heavy  concentrated 
load;  this  part  of  the  design  will  be  discussed  under  grillage  beams  (page 
293  :3).  The  amount  of  deflection  is  usually  immaterial  unless  the  beam 


the  deflection  should  be  determined  as  on  page  203  : 2. 

3.  Effects  of  Bending.  —  When  a  simple  horizontal  beam  is  loaded  it 
sags,  deflects,  or  bends  downward.  The  horizontal  fibers  in  the  lower 
part  of  the  beam  are  lengthened,  while  those  in  the  upper  part  are 
shortened;  between  these  two  parts  is  a  neutral  surface  in  which  the 
fiber  lengths  remain  unchanged.  Beams  are  designed  upon  the  assump- 
tion that  all  points  which  lie  in  a  transverse  plane  before  a  beam  is  bent 
remain  in  a  plane  after  the  beam  is  bent.  In  any  fiber  the  "strain" 
or  the  change  in  length  is  proportional,  within  the  elastic  limit,  to  the 
"  stress  "  or  internal  force  which  causes  the  strain,  according  to  Hooke's 
law.  The  unit  stresses  used  in  the  design  of  beams  are  well  within  the 
elastic  limit  (page  10)  and  this  relation  has  been  found  by  experi- 
ments to  be  true.  It  follows,  therefore,  that  the  horizontal  fiber  stresses 
are  proportional  to  the  distances  of  the  fibers  from  the  neutral  surface. 
Stresses  which  tend  to  lengthen  the  fibers  are  called  tensile  stresses  and 
the  fibers  are  said  to  be  in  tension;  similarly,  compressive  stresses  tend 
to  shorten  the  fibers  which  are  in  compression.  When  a  beam  is  con- 
sidered cut  by  an  imaginary  transverse  section  plane  the  external  forces 
acting  upon  either  segment  are  not  in  equilibrium  by  themselves  but 
they  are  held  in  equilibrium  by  the  internal  forces  acting  in  the  fibers 
which  are  cut  by  the  section  plane.  The  intersection  of  the  neutral  sur- 
face by  this  section  plane  is  termed  the  neutral  axis  of  this  cross  section; 
this  neutral  axis  passes  through  the  center  of  gravity  of  the  cross  section. 


197 


198 


PART   III  — THE   DESIGN   OF  DETAILS 


For  convenience  let  us  consider  a  simple  horizontal  beam  with  vertical 
loads.  This  simplifies  the  phraseology  and  covers  the  great  majority 
of  beams;  the  principles  can  be  readily  adapted  to  other  conditions. 
The  internal  force  in  each  fiber  cut  by  the  section  plane  may  be  resolved 
into  horizontal  and  vertical  components,  the  latter  all  acting  in  the  same 
direction.  The  sum  of  the  vertical  components  must  equal  numerically 
the  shear  on  the  segment,  because  the  algebraic  sum  of  the  vertical  com- 
ponents of  these  internal  forces  and  the  vertical  components  of  the  external 
forces  (i.e.,  the  shear,  page  184: 1 )  must  equal  zero  in  order  to  satisfy 
the  V  equation  of  equilibrium.  In  like  manner  the  H  equation  is  satis- 
fied when  the  algebraic  sum  of  the  horizontal  components  of  both  ex- 
ternal and  internal  forces  equals  zero;  since  there  are  no  horizontal 
components  of  external  forces  it  follows  that  the  sum  of  the  horizontal 
compressive  stresses  above  the  neutral  axis  must  equal  numerically  the 
sum  of  the  horizontal  tensile  stresses  below  the  neutral  axis.  In  order 
to  satisfy  the  M  equation  the  resisting  moment  or  the  sum  of  the  moments 
of  the  stresses  in  the  fibers  cut  by  the  section  plane  must  equal  numeri- 
cally the  bending  moment  or  the  sum  of  the  moments  of  the  external 
forces  acting  on  the  segment  (page  184  : 2).  Since  the  point  of  moments 
is  taken  in  the  section  plane  (page  184  : 2),  the  lever  arm  of  the  vertical 
components  of  the  internal  forces  is  zero,  so  only  the  horizontal  compo- 
nents need  be  considered.  The  significance  of  these  points  will  now  be 
discussed  in  detail. 

1.  Resisting  Moment  —  Theory.  —  A   portion   of  a  beam   cut  by   a 
vertical  section  is  shown  in  Fig.  198,  the  right-hand  portion  of  the  beam 

being  removed.     The  inclined  line  shows  the 
relative  position,  greatly  exaggerated,  of  the 
same  section  after  the  beam  is  bent.     The 
arrows  indicate  the  horizontal  components 
of  the  stresses  in  the  fibers  cut  by  the  sec- 
i    tion,  being  proportional   to  their  distances 
Fig.  198.  from  the  neutral  axis.     The  vertical  com- 

ponents are  not  shown  because  they  do  not 

enter  into  the  resisting  moment  (see  preceding  paragraph).  The  fiber 
which  is  farthest  from  the  neutral  axis  (either  in  tension  or  compression) 
is  stressed  the  most  and  consequently  its  strength  determines  the  strength 


of  the  beam.    The  unit  stress  in  this  extreme  fiber  must  not  exceed  the 
allowed  unit  stress  for  bending. 

Let         /  =  the  allowed  stress  in  the  extreme  fiber,  in  pounds  per  square 

inch, 

a  =  the  area  of  each  fiber,  in  square  inches, 
c  =  the  distance  from  the  neutral  axis  to  the  extreme  fiber,  in 

inches,  and 
x  =  the  distance  from  the  neutral  axis  to  any  fiber,  in  inches. 

Then    fa  =  the  stress  in  the  extreme  fiber, 

fax 

-  =  the  stress  in  any  fiber  at  a  distance  x  from  the  neutral 
c 

fax2 

— -  =  the  moment  of  this  stress, 
c 

fax2      f 

S  —  =  -  S  ax2  =  the  sum  of  the  moments  of  the  stresses  in  all  the 
c         c 

fibers  in  the  cross  section,  i.e.,  the  resisting  moment. 
But  the  expression  sax2  is  generally  recognized  as  the  moment  of 
inertia  *  of  the  cross  section  represented  by  /,  therefore 

—  -  MR  =  the  general  expression  for  the  resisting  moment  of  any  homo- 
geneous beam. 

2.  In  the  above  expression  for  resisting  moment  the  unit  stress  /  de- 
pends upon  the  material  of  which  the  beam  is  to  be  made.  Values  for 
/  must  be  taken  from  the  specifications  which  govern  any  specific  design. 
For  convenience,  the  values  recommended  by  the  American  Railway 
Engineering  Association  for  wood  are  given  on  page  320  and  for  steel 
on  page  317.  The  values  for  wood  are  for  a  better  grade  of  lumber 
than  is  often  used  and  the  values  allowed  by  the  building  laws  of  many 
cities  are  correspondingly  lower.  The  unit  stresses  for  steel  have  been 
quite  generally  adopted,  although  higher  values  are  allowed  for  higher 
grade  steel  used  in  large  bridges.  These  values  for  /  are  intended  only 
for  beams  which  are  properly  stayed  against  lateral  flexure  (page  201  :2). 

*  See  Kirkham's  "Structural  Engineering,"  McGraw-Hill  Book  Co.,  Inc.,  New  York, 
or  almost  any  book  on  the  Calculus  or  Mechanics.  For  a  proof  without  the  Calculus, 
see  page  199  :  3. 


CHAPTER  XXXI 


THE   DESIGN   OF  BEAMS 


199 


1.  Section  Modulus.  —  The  I  and  the  c  in  the  expression  for  resisting 
moment  both  depend  upon  the  form  of  the  cross  section  of  the  beam. 

Values  of  -  may  be  tabulated  for  different  cross  sections  regardless  of 
,  c 

the  unit  stress.    This  quantity  -  is  called  the  "  section  modulus  "  and  is 

often  represented  by  the  letter  S.  In  this  book  the  lower-case  letter  s 
will  be  used  consistent  with  the  adoption  of  lower-case  letters  for  units 
which  involve  inches,  and  capitals  for  those  which  involve  feet.  Hence 
ffiR  =  fs.  The  section  moduli  for  different  sections  are  found  in  the  com- 
mon handbooks  of  the  steel  manufacturers  and  also  in  the  tables  at  the 
end  of  this  book,  as  explained  below. 

2.  Units.  —  An  expression  for  resisting  moment  may  be  equated  to 
an  expression  for  bending  moment  provided  they  are  in  the  same  units, 


thus:    MB  =  MR  or  m,B  = 


whence  mg  =  —  .     Beams  are  usually  of 


constant  cross  section  and  they  are  therefore  designed  for  the  maximum 
bending  moment.  If  a  beam  is  of  variable  cross  section,  such  as  an  I-beam 
with  plates  riveted  to  the  flanges  along  the  central  part  of  the  beam, 
the  resisting  moment  at  any  section  must  satisfy  the  maximum  bending 
moment  that  can  occur  at  that  section.  In  the  above  equation,  or 
"  flexure  formula  "  as  it  is  sometimes  called,  there  can  be  only  one  un- 
known quantity  but  that  may  be  on  either  side  of  the  equation.  If  the 

section  modulus  (  s  =  -  1  is  unknown  the  problem  is  one  in  design,  other- 

wise it  is  one  in  investigation.    In  design  it  is  desired  to  find  the  shape 

wind  size  of  a  beam  which  will  meet  given  requirements.    In  investigation 

it  is  desired  to  find  how  great  a  load  a  given  beam  will  support,  how  great 

i!  i  distance  the  beam  will  span,  how  far  from  the  support  a  given  load 

may  be  placed,  or  how  great  a  unit  stress  is  developed.    The  usual  units 

lor  bending  moments  are  pound-feet  (page  184  :2)>  while  those  for  resist- 

ing moments  are   pound-inches  (compare   page  3:2).     These  must  be 

nade  identical  before  they  are  equated,  the  value  in  pound-feet  being 

nultiplied  by   12  to  give  pound-inches.     Lack  of  care  on  this  point 

Accounts  for  the  majority  of  all  mistakes  in  the  design  of  beams  by 

leginners.     A  convenient  method  of  determining  the  resulting  unit  of 


:.     This  method  can  be  applied  in  like  manner  to  expressions 


any  expression  such  as  that  for  resisting  moment  is  to  substitute  the 
units  of  the  component  parts  in  the  expression,  and  cancel  like  quan- 
tities which  occur  in  both  the  numerator  and  denominator.  This  can 
be  quickly  done  and  it  is  less  confusing  than  to  combine  the  units  and 
the  numerical  values  in  the  same  expression.  For  example,  in  the  expres- 
sion — ,  /  is  in  pounds  per  square  inch,  /  is  in  inches  to  the  fourth  power, 
c 

and  c  is  in  inches.    The  resulting  unit  is  pound-inches,  found  as  follows: 

#          ....  1  #in.  in.  in.  in.     „.    .. 

. — : —  x  in.  in.  in.  in.  x  .—  or  better  — — : — r .    Similarly,  the  unit  of 

in.  in.  in.  in.  in.  in. 

section  modulus  is  inches  cubed,  so  the  unit  of  fs  is  pound-inches  thus: 
#in.  in.  in. 

in.  in. 
for  bending  moment. 

3.  Rectangular  Beams.  —  The  moment  of  inertia  of  a  rectangle  is 

bd3 

r  where  d  is  the  dimension  at  right  angles  to  the  neutral  axis  and  b  the 
\.2i 

dimension  parallel  to  this  axis,  both  in  inches.    The  distance  c  from  the 

neutral  axis  to  the  extreme  fiber  is  ~  because  the  neutral  axis  through 

f 

the  center  of  gravity  passes  through  the  center  of  the  rectangle.  Sub- 
stituting these  values  in  the  general  expression,  we  find  the  resisting 

fbd2 
moment  of  a  beam  of  rectangular  cross  section  to  be  "j-j  whence  the 

6d2 
section  modulus  is  -^-.     This  expression  for  resisting  moment  may  be 

derived  independently  without  the  use  of  the  Calculus.  The  forces  above 
the  neutral  axis  (Fig.  198)  may  be  replaced  by  a  single  resultant  force. 
The  unit  stress  at  the  extreme  fiber  is  /  and  at  the  neutral  axis  zero.  Be- 
tween these  two  the  forces  vary  directly  with  the  distance  from  the  neutral 
axis  (page  198:1).  For  unit  breadth  the  sum  of  these  forces  is  equivalent 

to  the  area  of  a  triangle  the  base  of  which  is  /,  and  the  altitude  ^.    For  a 

& 

beam  of  breadth  6  the  magnitude  of  this  resultant  compressive  force 

is  „  X  /  X  5  X  6  which  acts  at  the  center  of  gravity  of  the  triangle  or 
4  - 


200 


PART   III  — THE   DESIGN   OF  DETAILS 


„  X  ~  below  the  top  of  the  beam.  Similarly,  the  forces  below  the  neutral 
o  ^ 

axis  may  be  replaced  by  a  single  resultant  tensile  force  equal  in  magni- 
tude to  the  resultant  compressive  force  and  acting  at  a  corresponding 
distance  above  the  bottom  of  the  beam.  These  two  equal  and  opposite 
forces  form  a  "  couple,"  the  moment  of  which  about  any  point  of  mo- 
ments is  equal  to  the  product  of  one  force  and  the  perpendicular  dis- 
tance between  the  two  forces.  This  moment  is  the  resisting  moment  of 

the  beam  and  is  equal  to   \fbd  x  (d  -2  x  5)  =  -^- .     This  expression 

V  6/6 

applies  to  homogeneous  beams  only;  it  does  not  apply  to  compound 
beams,  such  as  reinforced  concrete  beams.  Most  of  the  homogeneous 
rectangular  beams  which  are  designed  by  the  structural  designer  are 
wooden  beams.  These  beams  are  quite  often  designed  according  to 
nominal  dimensions,  but  it  seems  wiser  and  more  logical  to  use  the  actual 
dimensions  which  in  many  cases  are  considerably  less.  This  depends 
upon  the  custom  followed  in  the  saw  mills  of  the  different  localities.  By 
some  the  full  nominal  dimensions  are  furnished,  while  by  others  the 
width  of  each  saw  cut  is  deducted.  If  beams  are  planed,  further  deduc- 
tion is  made.  The  designer  should  be  cognizant  of  the  customs  of  the 
lumber  mills  which  are  most  likely  to  furnish  his  material.  In  the  absence 
of  further  information  the  following  quite  common  grading  rules  may 
be  used:  rough  sawed  beams  must  be  accepted  if  not  more  than  \"  scant 
on  each  dimension,  as  5|  X  llf ;  surfacing  or  planing  removes  an  addi- 
tional 5"  for  each  face  surfaced,  as  5f  x  llf  if  surfaced  on  one  side  and 
one  edge  (indicated  S1S1E),  or  5j  X  11|  if  surfaced  on  all  four  sides 
(indicated  S4S).  Tables  of  section  moduli  for  both  nominal  and  actual 
dimensions  are  given  on  page  319.  In  each  case  the  beam  is  known  by 
its  nominal  size  and  is  so  referred  to.  In  general  there  will  be  several 
different  sizes  of  beams  which  will  furnish  a  required  section  modulus, 
unless  one  dimension  is  determined  by  fixed  conditions,  as  for  example, 
when  a  beam  must  be  of  the  same  depth  as  another  similar  beam.  In 
case  a  table  of  section  moduli  is  not  available,  a  value  of  d  (or  6)  must  be 
assumed  and  the  corresponding  value  of  b  (or  d)  calculated.  Several 
trials  may  be  made  before  a  properly  proportioned  beam  results.  A 
knowledge  of  the  stock  sizes  of  the  locality  will  assist  in  the  selection 


of  the  beam  to  be  used.     The  position  in  the  structure,  the  method  of 
support,  and  the  tendency  to  overturn  or  to  buckle  transversely  mus 
all  be  considered.     The  deeper  beams  deflect  less,  are  stiffer,  and  ha^v 
a  smaller  cross  section  for  the  same  strength,  but  they  are  more  liabL 
to  overturn  and  they  may  not  have  sufficient  bearing  area  to  properlj 
distribute  the  loads  (page  203:1).     In  general  the  depth  should  be  from 
lj  to  2  times  the  breadth. 

1.  For  cylindrical  beams  of  circular  cross  section  7  =  — ,  and  c  =  - 

fad* 

where  d  is  the  diameter  in  inches.     The  resisting  moment  niR  =  ^p 

=  0.098/c?3  and  the  section  modulus  s  =  ~  =  0.098d3. 

2.  Steel  Beams.  —  In  determining  the  moments  of  inertia  of  I-beams 
channels,  angles,  and  other  structural  shapes,  the  curves  are  neglected 
It  is  unnecessary  for  the  designer  to  use  the  cumbersome  expressions  : 
for  the  moments  of  inertia  of  these  cross  sections  because  numerica 
values  for  7  and  for  s  about  axes  perpendicular  to  each  other  are  tabu 
lated  in  the  common  handbooks  and  in  this  book  (pages  322  to  326) 
I-beams  and  channels  are  regularly  placed  with  their  webs  parallel  t< 
the  applied  forces.    In  the  selection  of  a  steel  I-beam  or  channel  to  satisf; 
a  given  section  modulus,  preference  should  be  given  to  the  weights  printei 
in   larger   type   because  these   sections   can  usually   be   obtained  mor 
readily  from  the  mills.    Furthermore,  it  will  happen  frequently  that  thes 
beams  will  weigh  less  per  foot  and  therefore  cost  less  than  some  othe 
sizes  of  the  same  strength.    Sometimes  beams  must  be  of  the  same  dept 
as  some  other  beams,  and  it  is  usually  of  advantage  to  reduce  to  a  mini 
mum  the  number  of  different  sizes  of  beams  for  any  one  contract.    Th 
practical  designer  should  keep  posted  upon  market  conditions  and  kno' 
which  sizes  are  most  easily  and  quickly  obtained. 

3.  Every  beam  must  be  self  supporting,  and  this  fact  must  be  coi 
sidered  in  the  design.     Since  the  weight  of  a  beam  is  not  known  until  aft( 
the  beam  is  designed,  the  weight  must  be  assumed  and  the  correspondir 
bending  moment  must  be  combined  with  the  bending  moment  for  tl 
other  dead  and  live  loads.    This  is  simpler  than  to  attempt  to  carry  tl  > 

*  These  expressions  are  given  in  the  Handbook  of  the  Cambria  Steel  Company. 


CHAPTER  XXXI 


THE  DESIGN  OF  BEAMS 


201 


weight  of  the  beam  in  terms  of  the  unknown  dimensions.  After  the 
size  of  the  beam  is  determined  the  actual  weight  should  be  compared 
with  the  assumed  weight  and  the  design  should  be  corrected  accordingly, 
if  necessary.  Usually  the  bending  moment  due  to  the  weight  of  the 
beam  forms  a  small  portion  of  the  total  bending  moment,  so  that  a  slight 
discrepancy  does  not  matter.  Whether  or  not  the  difference  in  weight 
is  great  enough  to  affect  the  design  can  usually  be  told  by  inspection. 
It  does  not  take  much  experience  to  enable  one  to  estimate  the  weight 
more  closely  than  if  neglected  altogether  and  there  is  a  good  chance  of 
one's  guessing  accurately  enough  to  make  a  redesign  unnecessary.  In 
estimating  the  weight  of  a  wooden  beam  it  is  usual  to  allow  3J,  4,  4|, 
or  5  pounds  per  foot  board  measure,  the  last  two  being  for  creosoted  wood. 
One  "  foot  board  measure  "  (Ft.B.M.)  is  one-twelfth  of  a  cubic  foot, 
as  in  a  board  one  foot  square  and  one  inch  thick.  To  obtain  the  number 
of  feet  board  measure  in  a  piece  of  timber  take  two  dimensions  in  feet 
and  one  in  inches.  Four  pounds  per  foot  is  an  average  value  for  struc- 
tural timber.  If  the  dimensions  of  the  cross  section  (6  and  d)  are  taken 

in  inches  the  weight  of  a  beam  per  linear  foot  is  4  x  1  X  775  or  -5-. 

I  —  o 

Upon  this  basis  the  weights  in  the  last  column  on  page  319  are  obtained. 

1.  A  beam  is  weakened  by  holes.  —  The  size  of  the  beam  is  determined 
by  the  maximum  bending  moment.    Since  a  beam  is  generally  of  uniform 
cross  section  throughout  its  length  there  is  an  excess  in  area  except  near 
the  point  of  maximum  bending  moment.     Where  this  excess  is  large, 
as  for  example  near  the  ends  of  a  simple  beam,  holes  may  be  safely  punched 
or  bored.    W'hen  holes  are  required  in  wooden  beams  or  in  the  flanges 
of  steel  beams  where  the  bending  moment  is  nearly  maximum  their 
effect  should  be  considered.     The  moment  of  inertia  of  the  net  section 
should  be  used.    This  may  be  found  by  subtracting  the  moment  of  inertia 
of  the  holes  from  the  moment  of  inertia  of  the  cross  section  about  the 
same  neutral  axis. 

2.  Lateral  Supports.  —  Steel  beams  are  designed  for  the  usual  unit 
stress  of  16,000#/sq.  in.  in  bending  only  upon  the  assumption  that  they 
ire  properly  stayed  laterally  so  that  the  compression  flanges  will  not 
buckle.     Such  lateral  support  may  be  furnished  by  wooden  flooring  or 
sheathing,  by  any  form  of  solid  floor  construction,  by  masonry  walls, 


by  tie  rods,  by  special  struts,  by  lattice  bars  or  tie  plates,  by  separators, 
diaphragms,  etc.  In  the  absence  of  some  such  support  the  allowed  unit 
stress  should  be  reduced  according  to  the  ratio  of  the  distance  (I)  between 
lateral  supports  to  the  extreme  width  of  member  (6).  The  American 
Railway  Engineering  Association  specifies  that  the  maximum  stress  in 

the  compression  fibers  must  not  exceed  16,000  -  200r.     For  the  sake 

of  comparison,  numerical  values  are  tabulated  below  for  this  reduction 
formula,  and  also  for  the  formulas  recommended  by  R.  Fleming  *  of 
the  American  Bridge  Company,  by  the  Carnegie  Steel  Company,  and 
by  the  Cambria  Steel  Company.  No  value  should  exceed  16,000. 

UNIT  STRESSES  TOR  BEAMS  WITHOUT  LATERAL  SUPPORT 


Ratio 

A.R.E.A. 

Fleming 

Carnegie 

Cambria 

I 
b 

16,000-  200  j 

19,000  -  250  r 

0 

19,000  -  3(K)[ 
o 

18,000 

1    1        * 

1  30006' 

5 

15,000 

16,000 

16,000 

16,000 

10 

14,000 

16,000 

16,000 

16,000 

15 

13,000 

15,250 

14,500 

16,000 

20 

12,000 

14,000 

13,000 

15,880 

25 

11,000 

12,750 

11,500 

14,900 

30 

10,000 

11,500 

10,000 

13,850 

35 

9,000 

10,250 

8,500 

12,780 

40 

8,000 

9,000 

7,000 

11,740 

3.  Beams  which  are  subjected  to  a  lateral  thrust  should  receive  special 
consideration.  For  example,  a  floor  beam  next  to  an  elevator  shaft  or 
other  opening  may  receive  the  thrust  from  a  brick  or  tile  floor  arch  on 
one  side  only.  Intermediate  beams  have  the  thrust  of  one  arch  largely 
counterbalanced  by  that  of  the  arch  on  the  opposite  side.  The  thrust 
of  an  arch  at  the  ends  of  the  arch  span  is  equal  to  the  maximum  total 
compressive  stress  and  this  must  be  counteracted  by  the  tension  in  tie 
rods  or  by  the  lateral  resistance  of  the  beams.  Concrete  floor  slabs  are 
usually  reinforced  so  that  no  thrust  on  the  beam  need  be  considered. 
In  deriving  an  expression  for  thrust  in  pounds  per  linear  foot  of  beam 
*  Engineering  News,  April  6,  1916. 


202 


PART  III  — THE  DESIGN  OF  DETAILS 


let  us  assume  an  equal  tension  T  in  the  tie  rods,  also  in  pounds  per  linear 
foot  of  beam.  These  equal  forces  constitute  a  couple,  and  the  perpen- 
dicular distance  between  them  is  the  effective  depth  of  the  arch  h  in 
inches.  The  resisting  moment  Th  must  equal  the  bending  moment  on 
the  arch  due  to  a  vertical  load  of  U'  pounds  per  square  foot  for  a  span 

U'  I  X\ 

of  X  feet  center  to  center  of  beams,  thus  :    Th  =  12  -=-  (  7^  I2  whence  the 

*    \«/ 

3  U'  X2 
thrust  T  =  —  ^T  —  .    For  flat  arches  commonly  used,  the  effective  depth 

£ifa 

may  be  taken  2.4"  less  than  the  depth  of  the  arch.  A  beam  without 
lateral  support  must  be  designed  so  that  the  combined  fiber  stress  due 
to  vertical  bending  and  to  lateral  bending  will  not  exceed  the  allowed 
stress  per  square  inch  (16,000).  A  beam  somewhat  larger  than  the  size 
required  for  vertical  forces  alone  should  be  assumed  and  then  investi- 
gated. The  fiber  stress  due  to  vertical  forces  may  be  found  by  equating 
the  bending  moment  of  vertical  forces  to  the  resisting  moment  and  solv- 
ing for  /,  the  section  modulus  of  the  assumed  beam  being  known.  Simi- 
larly, the  fiber  stress  due  to  lateral  forces  may  be  found,  the  bending 
moment  being  found  for  the  uniformly  distributed  thrust  T  (see  above) 
and  for  the  proper  length  between  supports.  The  section  modulus  must 
be  taken  about  an  axis  parallel  to  the  web.  Values  for  this  s2  for  channels 
are  given  on  page  323.  Values  for  I-beams  may  be  obtained  from  72 
(page  322)  and  from  c  which  is  one-half  the  flange  width.  (Note  that 
c  for  channels  is  the  distance  from  the  center  of  gravity  to  the  further 
edge  of  the  flange.)  If  a  beam  is  supported  by  tie  rods  it  becomes  a  con- 
tinuous beam.  By  the  Theorem  of  Three  Moments  an  expression  *  may 
be  found  for  the  maximum  lateral  bending  moment  in  terms  of  the  thrust 
T  and  the  panel  length  B  between  rods.  If  only  one  rod  is  used  in  the 

TB2 
center  of  the  span  L,  the  bending  moment  is  —5-;  if  two  rods  are  used 

o 

TB* 
making  three  equal  panels  of  B  feet  the  bending  moment  is  -r  ;  if  three 


rods  are  used  making  four  equal  panels  the  bending  moment  is 


o  rrt  T>2 


1.  Shear.  —  After  a  beam  is  designed  to  give  proper  resistance  to 
bending,  its  resistance  to  shear  should  be  investigated.  The  size  of  the 
beam  will  seldom  be  increased  as  a  result  of  this  investigation,  neverthe- 
less it  should  be  disregarded  only  by  a  man  of  experience  when  he  is  con- 
fident that  no  increase  will  result.  The  intensity  of  vertical  shear  at  any 
point  of  a  beam  is  equal  to  the  intensity  of  horizontal  shear  at  the  same 
point,  f  much  as  the  vertical  and  the  horizontal  water  pressures  at  any 
point  in  a  tank  of  water  are  equal.  This  intensity  is  not  uniform  through- 
out the  cross  section  but  is  zero  at  the  extreme  fibers  and  maximum  at 
the  neutral  axis.  The  maximum  shear  intensity  in  any  beam  should 
not  exceed  the  allowed  unit  stress  either  in  horizontal  shear  or  in  vertical 
shear.  For  steel  the  allowed  stresses  are  equal,  but  for  wood  the  value 
specified  for  the  "  longitudinal  shear  in  beam  "  is  considerably  less  than 
for  the  transverse  shear.  For  any  cross  section  of  a  rectangular  beam 
the  maximum  shear  intensity  is  three-halves  of  the  average  shear  in- 

3F 

tensity,  or  v  =  =r-,,  in  which  v  =  maximum  horizontal  or  vertical  shear 


*  See   Johnson-Bryan-Turneaure's    "Modern   Framed  Structures,"   Part    II,   John 
Wiley  and  Sons,  Inc.,  New  York.     See  also  footnote,  page  193. 


intensity  in  pounds  per  square  inch,  V  =  maximum  shear  for  the  section  in 
pounds,  6  and  d  =  the  breadth  and  depth  of  the  beam  in  inches.  This  ex- 
pression may  be  derived  in  the  following  manner.  In  Fig.  198  are  shown  the 
horizontal  forces  acting  in  the  fibers  of  a  beam  cut  by  a  transverse  section. 
Let  a  similar  section  be  passed  at  a  small  distance  x  from  the  first  section 

Let     /i  =  the  unit  stress  in  the  extreme  fiber  at  the  first  section, 
/2  =    "      "        "      "     "         "          "      "    "    second     " 

c  =    -  =  the  distance  from  the  neutral  axis  to  the  extreme  fiber. 
2i 

mi  =  fis  =  the  bending  moment  at  the  first  section, 

mz  =  /2S  =    "        "  "        "    "    second     " 

m2  =  mi  +  Vx  (page  189  :  1),  the  shear  virtually  being  constant  betweei 

sections, 
hfP 
s  =  ^-  (page  199  :  3). 

/2  -  /i  =  the  increase  in  stress  in  the  extreme  fiber  within  the  distance  a 

t  See  Kirkham's  "Structural  Engineering,"  McGraw-Hill  Book  Co.,  Inc.,  New  Yort 
Fuller  and  Johnston's  "Applied  Mechanics,"  Vol.  II,  John  Wiley  and  Sons,  Inc.,  Ne' 
York,  or  similar  books. 


CHAPTER  XXXI 


THE  DESIGN   OF  BEAMS 


203 


There  is  a  proportionate  increase  in  every  fiber  between  the  'extreme 
fiber  and  the  neutral  axis.  The  longitudinal  shearing  stress  at  the  neutral 
axis  for  the  distance  x  per  unit  of  breadth  is  the  sum  of  the  increases  in 
stress  in  all  these  fibers.  This  sum  is  equivalent  to  the  area  of  a  triangle 

of  which  the  base  is  /2  -  fi  and  the  altitude  ~.    The  shearing  stress  per 

a 

square  inch  or  the  shear  intensity  is  equal  to  this  sum  divided  by  x,  or 


V  = 


d 
2 


+  Vx  -nil) 


3V 
2bd' 


The  general  expression*  for  the  shear  intensity  at  any  point  of  a  beam 


of  any  cross  section  is  v  =-•  -~,  in  which  q 


the  statical  moment  about 


follows:  v  = 


For  beams  of  circular  cross  section  the 


the  neutral  axis  of  that  portion  of  the  cross  section  between  a  horizontal 
plane  through  the  extreme  fiber  and  a  horizontal  plane  through  the  given 
point,  and  b  =  the  breadth  of  the  beam  where  cut  by  the  latter  plane. 
The  statical  moment  is  the  product  of  the  area  of  the  portion  of  the  cross 
section  referred  to  by  the  distance  from  its  center  of  gravity  to  the  neutral 
axis.  Thus  the  expression  for  the  maximum  shear  intensity  at  the  center 
•of  a  rectangular  beam  may  be  found  from  the  general  expression  as 
rvW  d 

2*  4_   3F 

_3  x  b      =  2bd' 

12 
maximum   shear   intensity   is   four-thirds   of   the   average   intensity   or 

16F       4F 
v  =  ^— T2  =  5 — j  in  which  d  and  r  =  the  diameter  and  the  radius  of  the 

beam  in  inches.  For  I-beams  and  channels  there  is  no  convenient  expres- 
sion for  the  maximum  shear  intensity,  nor  can  the  intensity  be  found 
without  considerable  computation. f  For  all  practical  purposes,  however, 
it  is  sufficiently  accurate  to  use  an  approximate  method  which  can  be 
applied  much  more  easily.  The  web  must  furnish  most  of  the  resistance 

*  See  Fuller  and  Johnston's  "Applied  Mechanics,"  Vol.  II,  John  Wiley  and  Sons, 
Inc.,  New  York. 

t  See  Fuller  and  Johnston's  "Applied  Mechanics,"  Vol.  II,  John  Wiley  and  Sons, 
Inc.,  New  York,  or  the  Carnegie  Steel  Company's  "Pocket  Companion." 


to  shear  because  the  flange  areas  are  concentrated  near  the  extreme  fibers 
where  the  shear  intensity  is  small.  The  maximum  shear  intensity  for 
an  I-beam  or  a  channel  may  be  found  by  dividing  the  maximum  shear 
V  by  the  area  of  the  straight  portion  of  the  web  between  the  flanges. 
This  area  is  equal  to  the  web  thickness  multiplied  by  the  tangent  dis- 
tance (d-2k  from  the  tables)  between  the  curved  fillets. 

1.  Bearing.  —  A  beam  which  rests  upon  its  supports  must  have  suf- 
ficient bearing  area  to  properly  distribute  the  pressure  of  the  beam  on 
the  supporting  wall,  beam,  or  column.     A  beam  which  rests  upon  ma- 
sonry walls  usually  has  a  steel  or  cast-iron  bearing  plate  to  provide 
greater  bearing  area.    The  design  of  such  a  bearing  plate  is  explained  in 
Chapter  XLIII,  page  288.     The  bearing  is  not  a  determining  factor  in 
other  methods  of  support  for  steel  beams,  such  as  connection  angles  with 
rivets.    The  bearing  does  play  an  important  part  in  the  design  of  wooden 
beams  because  it  may  determine  the  width  of  the  supported  beam  or  the 
width  of  the  beam  or  column  which  supports  it.     The  bearing  area  or  the 
horizontal  area  of  contact  between  a  beam  and  its  support  must  be 
large  enough  to  prevent  the  fibers  from  crushing.     The  allowed  pressure 
per  square  inch  is  the  unit  stress  in  "  crushing  "  or  compression  at  right 
angles  to  the  grain.    The  total  pressure  is  equal  to  the  maximum  reaction 
which  can  be  caused  by  the  full  dead  load  (including  the  weight  of  the 
beam)  and  the  live  load.    The  required  bearing  area  is  found  by  dividing 
this  total  pressure  by  the  unit  stress  in  crushing  across  the  grain.    The 
necessary  length  of  bearing  or  the  distance  which  the  beam  must  project 
onto  the  support  is  found  by  dividing  the  bearing  area  by  the  width  of 
the  supported  beam.     If  two  beams  are  supported  at  the  same  point 
of  a  supporting  beam,  the  width  of  the  latter  must  be  sufficient  to  furnish 
the  proper  length  of  bearing  for  both  beams.     Sometimes  two  narrow 
joists  or  beams  overlap  so  that  each  may  bear  on  more  than  one  half  the 
width  of  the  supporting  beam. 

2.  Deflection.  —  The  amount  of  vertical  deflection  is  an  important 
consideration  only  in  the  design  of  beams  which  support  tile  or  concrete 
floors,  plastered  ceilings,  shafting,  etc.     If  the  deflection  exceeds  a  cer- 
tain amount,  unsightly  cracks  are  liable  to  result  in  the  floors  or  ceilings, 
and  free  action  of  the  shafting  or  other  moving  parts  may  be  impaired. 
Certain  limiting  ratios  of  the  depth  to  the  length  of  a  beam  can  be  found, 


204 


PART   III  — THE   DESIGN   OF   DETAILS 


above  which  a  beam  will  not  have  excessive  deflection.  By  means  of 
these  ratios  the  designer  can  properly  design  beams  without  further 
investigation  for  deflection.  Accordingly,  the  theory  of  the  elastic  curve 
will  not  be  developed  here,*  but  sufficient  formulas  will  be  given  to  enable 
the  student  to  determine  the  amount  of  deflection  in  the  average  beam. 
In  all  of  these  expressions,  L  =  the  effective  length  of  the  beam  in  feet, 
I  =  the  same  in  inches,  P  =  the  concentrated  load  in  pounds,  U  =  the 
unit  load  uniformly  distributed  in  pounds  per  linear  foot,  W  =  the  cor- 
responding total  load  uniformly  distributed  in  pounds,  I  =  the  moment 
of  inertia  of  the  cross  section  in  inches4,  and  E  =  the  modulus  of  elas- 
ticity in  pounds  per  square  inch.  The  modulus  of  elasticity  for  steel  is 
29,000,000;  values  for  different  kinds  of  wood  are  given  on  page  320. 
The  maximum  deflection  in  inches  at  the  center  of  a  simple  beam  under 


a  full  load  uniformly  distributed  is 
load  concentrated  at  the  center  is 


5W13        45C7Z/4 


,  and  under  a  single 


PI3        36P7/3 


The  maximum  de- 

flection  in  inches  at  the  free  end  of  a  cantilever  beam  supported  at  one 

Wl3      216  UL4 
end   only   under   a   full   load   uniformly   distributed   is 


PI3       576PL3 
and  under  a  single  load  concentrated  at  the  free  end  is  • 


For  beams  with  combined  loads  the  deflection  due  to  concentrated  loads 
and  uniformly  distributed  loads  may  be  added.  It  has  been  determined 
experimentally  that  plaster  will  crack  when  the  deflection  is  more  than 
of  the  span,  and  this  value  appears  in  many  specifications.  If  we 


12L  ,     45  f/L4  36PL3 

equate  -^r  to        „.     or  to  —  =y—  and  eliminate    U  or  P  as  explained 
2iCi  L  EJ  I 


below,  we  can  solve  for  the  corresponding  ratio  of  the  depth  to  the  length. 

12  t/L2        12PL  fl      2/7  4/7 

By  equating  WB  =  — ^ —  or  — j —  to  TOR  =  - —  =  -V  we  find  (/  =  ^y- 

^^T-    By  substituting  these  values  above  and  also  E  =  29,000,000 

ouJL/ 


and  P  = 


*  See  Fuller  and  Johnston's  "Applied  Mechanics,"  Vol.  II,  John  Wiley  and  Sons, 
Inc.,  New  York;  or  Kirkham's  "Structural  Engineering,"  McGraw-Hill  Book  Co.,  Inc., 
New  York.  For  diagrams  by  C.  A.  Ellis,  see  Engineering  Record,  Jan.  15,  1916. 


and  /  =  16,000,  we  can  solve  for  -^j-  =  T.    In  this  manner  we  find  that 

/ 


for  simple  steel  I-beams  or  channels  designed  for  a  unit  stress  of  16,000#/sq. 
in.  in  bending,  and  a  modulus  of  elasticity  of  29,000,000#/sq.  in.,  the  de- 
flection will  not  exceed  ^  of  the  span  if  the  depth  is  at  least  -fa  of  the 
span  for  a  uniformly  distributed  load  or  at  least  ^  of  the  span  for  a 
single  concentrated  load  at  the  center.  In  other  words,  the  length  in 
feet  should  not  be  more  than  two  (or  two  and  one-half)  times  the  depth 
in  inches.  Other  ratios  can  be  derived  in  a  similar  manner  as  required. 
When  a  beam  is  subject  to  shocks  or  vibrations  the  depth  should  not 
be  less  than  TXF  the  span.  I-beam  stringers  for  railway  bridges  should 
preferably  have  a  depth  not  less  than  TV  of  the  span.  When  the  depth 
cannot  fulfill  the  above  conditions  the  beam  should  be  made  enough 
stronger  so  that  the  deflection  will  not  be  greater  than  if  a  beam  of  the 
required  depth  were  used.  Roof  purlins  may  usually  have  a  depth  of 
only  -jig-  of  the  span  because  the  maximum  load  is  seldom,  if  ever,  realized. 

1.  The  principal  points  of  this  chapter  are  illustrated  by  the  following 
typical  problems. 

First  Problem  —  Wooden  Beam.  —  Design  a  12-foot  Norway  Pine  beam  for 
a  building,  to  resist  a  bending  moment  of  12,500#ft.  and  a  shear  of  4,200#. 

12,500#ft.  =  bending  moment  of  superimposed  loads 

400#ft.  =  •%*-  X  62  =  bending  moment  due  to  weight  of  beam 

(6  x  12  assumed;   see  page  319  for  weight) 
12  X  12,900  =  1,200s  (for  unit  stress  in  bending,  see  page  320) 
129  =  s. 

Counting  the  actual  dimensions  \"  scant,  this  calls  for  a  6  x  12,  the 
section  modulus  for  a  5f  X  llf  being  132. 

4,200#  =  shear  due  to  superimposed  loads 
150#  =  24  x  6  =  shear  due  to  weight  of  beam 
3  X  4,350 


90#/sq.  in. 


2x5.75  X  12.75 


maximum  shear  intensity  (page  202:1). 


This  is  safely  under  the  150  allowed  for  longitudinal  shear  in  beams 
(page  320). 

4,350 


3.3' 


230  X  5.75 


=  the  length  of  bearing  required. 


CHAPTER  XXXI 


THE   DESIGN   OF  BEAMS 


205 


Second  Problem  —  Wooden  Beam.  —  Design  a  Long  Leaf  Yellow  Pine      12  x  12,800  =  16,000s  (for  unit  stress  in  bending,  see  page  317) 
(abbreviated  LLYP)  Highway  bridge  beam  20  feet  long  to  support  a 


uniformly  distributed  load  of  250#ft. 
8  x  12 


30#/ft.  = 
14,000#ft.  = 


3 

30  +  250 


weight  of  beam  8  X  12  assumed  (page  200  : 3) 
X  102  =  total  MB 


12  x  14,000  =  1,630s 

104  =  s  which  calls  for  a  6  x  12  or  an  8  X  10  although  both  are 
large. 


9.6  =  s. 

Either  a  7"  I  15#  (page  322)  or  a  9"  U  13£#  (page  323)  can  be  used. 
Note  that  an  8"  l_l  16j#  is  strong  enough,  but  it  weighs  more  and  is  not 
so  readily  obtained  (page  200  : 2) . 

4,200#  =  shear  due  to  superimposed  loads 

90#  =  15  x  6  =  shear  due  to  weight  of  7"  I  15# 
4,290 


3,270  = 


.25(7  -  2  x  |) 


shear  intensity  which  is  safely  under  the 


Since  a  6  x  10  is  nearly  large  enough  it  should  be  tried  because  the     l°,000#/sq.  «>.  allowed  for  beam  webs  as  well  as  for  girder  webs  (page 


reduced  weight  may  reduce  the  section  modulus  sufficiently. 

6  x  10 
20  =  — 5 —  =  revised  weight 


(30  -  20)  102  x  12 
2  x  1630 


=  the  reduction  in  s. 


100  =  104  -  4  =  the  revised  section  modulas.     A  6  x  10  can  there- 
fore be  used. 

2,700#  =  (20  +  250)10  =  maximum  shear. 
3  x  2,700 


68#/sq.  in.  = 


317). 

Fourth  Problem  —  Investigation.  —  Find  the  safe  load  concentrated  at 
the  center  which  a  15"  I  42#  30'-0"  can  support.  Also  find  the  maxi- 
mum deflection.  The  section  modulus  is  58.9  in.3  and  the  unit  stress 

p 

is  16,000#/sq.  in.    The  reaction  for  a  load  P  at  the  center  is  -~  and  the 

p 

bending  moment  =-x  15.     The  bending  moment   due  to  the  weight  of 

42 


1.2"  = 


2  X  6  X  10 

the  150  allowed. 
45  x  270  x  204 


45C/L4 


=  the  maximum  deflection. 


2  X 


=  maximum  shear  intensity  which  is  safely  under     *ne  beam  is  —  X  152.     Hence 

=  16,000  x  58.9 
/ 

2  x  1,610,000  X  500  "     2EI  9,840#  =  P. 

Third  Problem  —  Steel  Beam.  —  Design  a  steel  beam  to  satisfy  the     -75"  =  ^  n*n  ^m  ^M9   =      g^   =  deflection  due  to  concentrated  load. 

45  U. 


j...         .  .,     -  , ,        , 

conditions  of  the  first  problem  above. 

12,500#ft.  =  bending  moment  of  superimposed  loads 
300#ft.  =  ->jf  x  62  =  MB  of  assumed  weight  of  beam 


.06"  = 


29,000,000  x 

45  x  42  x  304         = 

2  x  29,000,000  X  442  =      2EI 


deflection  due  to  weight  of  beam. 


.81"  =  total  deflection. 


CHAPTER  XXXII 
THE    DESIGN    OF    TENSION    AND    COMPRESSION    MEMBERS 

SYNOPSIS:  The  principles  of  design  are  given  for  the  more  common  types  of  tension 
and  compression  members  and  for  lattice  bars.  No  attempt  has  been  made  to  cover 
the  practical  points  which  must  be  considered  in  the  design  of  a  complete  structure. 


1.  The  structural  designer  must  take  into  consideration  many  practical 
points.    He  must  not  design  each  member  independently  of  other  mem- 
bers, but  he  must  so  proportion  all  the  members  that  they  will  form  the 
best  complete  structure.     He  must  consider  not  only  the  strength  and 
the  appearance  of  each  member,  but  he  must  also  anticipate  the  details 
so  that  the  member  can  be  fabricated  and  connected  to  other  members 
to  the  best  advantage.     The  design  of  complete  structures  is  outside 
the  scope  of  this  book,*  but  the  fundamentals  of  design  are  here  given 
inasmuch  as  the  draftsman  is  often  called  upon  to  design  simple  members. 

2.  A  tension  member  is  designed  to  transmit  tensile  stresses  in  a  direc- 
tion parallel  to  its  principal  axis;    the  stresses  which  are  transmitted  by 
a  tension  member  tend  to  elongate  that  member.    A  compression  member 
is  designed  to  transmit  compressive  stresses  in  a  direction  parallel  to  its 
principal   axis;    the   stresses  which   are  transmitted  by  a  compression 
member  tend  to  shorten  that  member.     Sometimes  forces  are  applied  to 
either  tension  or  compression  members  which  tend  to  bend  them  trans- 
versely.   Such  members  must  be  designed  for  stresses  due  to  both  bending 
and  direct  tension  or  compression. 

*  For  more  complete  treatises  see  Johnson-Bryan-Turneaure's  "Modern  Framed 
Structures,"  Vol.  Ill,  John  Wiley  and  Sons,  Inc.,  New  York,  for  bridges  and  roof  trusses; 
Ketchum's  "Mill  Buildings,"  McGraw-Hill  Book  Co.,  Inc.,  New  York,  for  mill  building 
construction;  Burt's  "Steel  Construction,"  American  Technical  Society,  Chicago,  for 
office  building  construction;  Kirkham's  "Structural  Engineering,"  McGraw-Hill  Book 
Co.,  Inc.,  for  bridges,  mill  buildings,  and  office  buildings;  and  Kunz's  "Design  of  Steel 
Bridges,"  McGraw-Hill  Book  Co.,  Inc.,  for  viaducts,  movable  bridges,  arches,  canti- 
levers, etc. 


3.  The  area  of  cross  section  is  an  important  factor  in  the  design  of 
either  a  tension  or  a  compression  member,  while  the  form  of  cross  sec- 
tion  is   of  special   importance   in   a   compression   member.     A   tension 
member  is  equally  strong  whether  the  cross  section  is  in  the  compact 
form  of  a  circle  or  rectangle,  or  in  the  more  open  form  of  a  hollow  pipe 
or  similar  section,  provided  the  area  is  the  same.    A  compression  member, 
on  the  other  hand,  is  stronger  if  the  metal  is  distributed  so  that  the 
member  is  less  likely  to  buckle  or  bend  under  compression.    Thus  a  small 
rod  would  not  resist  so  much  compression  as  would  a  hollow  pipe  contain- 
ing the  same  amount  of  metal.    Cast  iron  columns,  for  example,  are  made 
hollow  for  this  reason. 

4.  Effect  of  Rivet  Holes.  —  A  tension  member  is  weakened  by  having 
holes  punched  in  it  for  rivets.    A  compression  member  is  not  weakened 
in  the  same  manner,  provided  the  rivet  holes  are  completely  filled  with 
either  shop  or  field  rivets.     The  reason  for  this  difference  is  that  the 
rivets  are  in  contact  with  the  metal  surrounding  the  holes,  but  they  are 
not  attached  to  this  metal.    The  rivets  in  the  holes  can  therefore  transmit 
compressive  stresses  from  one  side  of  the  hole  to  the  other  much  as  the 
original  metal  would,  but  the  rivets  cannot  prevent  the  member  from 
pulling  away  from  them  when  the  member  is  subjected  to  tensile  stresses. 
Rivets  are  compressed  in  driving,  so  the  effect  of  cooling  is  to  reduce  the 
resulting  pressure  in  the  rivets  rather  than  to  shrink  them  so  they  are 
no  longer  in  contact.     Bolts,  however,  do  not  completely  fill  the  holes. 
Any  bolt  holes,  or  holes  left  open,  should  be  considered  in  determining 
the  effective  area  of  a  compression  member,  provided  they  occur  when 


206 


CHAPTER  XXXII 


THE  DESIGN  OF  TENSION  AND   COMPRESSION  MEMBERS 


207 


there  is  considerable  tendency  to  buckle.  In  a  tension  member  it  is 
assumed  that  the  total,  stress  is  distributed  uniformly  over  the  net  area; 
in  a  compression  member  it  is  assumed  that  the  total  stress  is  distributed 
uniformly  over  the  whole  gross  area,  except  as  provided  in  the  preceding 
sentence.  These  assumed  conditions  are  not  always  fulfilled,  particu- 
larly when  the  end  connections  are  not  properly  designed;  but  the 
assumptions  have  proved  sufficiently  accurate  for  the  design  of  such 
members  as  are  discussed  in  this  chapter. 

TEtfSION   MEMBERS 

1.  A  tension  member  must  be  so  designed  that  it  is  strong  enough  at 
its  weakest  point  to  carry  the  total  stress.    Some  of  the  lightest  tension 
members  are  made  of  round  or  square  rods.      Different  methods  are 
employed  for  fastening  these  rods  to  other  members,  as  illustrated  on 
page  316. 

2.  A  loop  rod  is  made  by  bending  the  end  of  a  rod  back  upon  the  rod 
and  forging  it  to  form  a  loop  (page  316).     The  loop  is  shaped  to  fit 
around  a  pin  such  as  a  cotter  pin  (Fig.  279)  or  a  larger  pin  (Fig.  278  (6)). 
The  loops  are  made  stronger  than  the  main  part  of  the  rod,  so  that  the 
designer  simply  has  to  determine  the  size  of  the  rod.    Both  round  and 
square  rods  are  used  for  loop  rods.     The  required  area  of  cross  section 
is  found  by  dividing  the  total  stress  by  the  allowed  unit  stress.     From 
the  table  on  page  315  the  diameter  of  a  commercial  size  of  round  rod  may 
be  selected  with  an  area  (second  column)  which  equals  or  exceeds  the 
required  area.     The  size  of  a  square  rod  may  be  found  by  taking  the 
square  root  of  the  area  or  by  using  tables  of  square  rods  found  in 
the  handbooks  of  the  different  steel  manufacturers.    The  sizes  most  used 
are  multiples  of  £". 

3.  A  clevis  is  a  forging  made  with  two  loops  between  which  a  con- 
necting plate  is  inserted  and  held  in  place  by  a  cotter  pin.    The  clevis 
is  made  to  screw  on  the  end  of  the  rod  like  a  nut,  a  right-hand  thread 
being  used  at  one  end  and  a  left-hand  thread  at  the  other  so  that  when 
the  rod  is  turned  it  is  tightened.    Clevises  are  used  less  frequently  than 
formerly  because  of  the  relatively  high  cost. 

4.  The  form  of  rod  most  used  is  the  round  rod  threaded  at  the  ends 
for  nuts,  as  shown  in  the  different  types  of  connection  on  page  316.    The 


effective  area  of  the  rod  is  reduced  when  a  thread  is  cut  and  a  corre- 
spondingly larger  rod  must  be  used  so  that  the  least  area  at  the  root 
of  the  thread  will  be  sufficient.  In  most  cases  a  larger  rod  is  used  for 
the  entire  length.  The  ends  of  some  of  the  longer  rods  are  upset  in  the 
forge  shop  to  a  larger  diameter  so  that  after  the  threads  are  cut  the 
strength  at  the  ends  is  slightly  greater  than  the  strength  of  the  main 
portion  of  the  rods.  The  diameters  and  lengths  of  standard  upset  ends 
are  given  on  page  315.  The  design  of  an  upset  rod  is  the  same  as  for  a 
loop  rod,  only  the  main  portion  of  the  rod  being  considered.  The  table 
of  root  areas  for  the  upset  ends  may  be  used  in  the  design  of  rods  which 
are  threaded  without  being  upset.  For  example,  let  us  design  a  rod  to 
carry  a  stress  of  7,500#  at  a  unit  stress  of  16,000#/sq.  in.  The  net  area 
must  be  at  least  0.47  sq.  in.  =  7500  -=-  16,000.  The  diameter  of  a  rod 
with  a  root  area  of  0.55  is  1",  which  must  be  used  as  the  next  smaller 
rod  has  a  root  area  of  only  0.42.  Note  that  a  loop  rod  or  an  upset  rod 
used  under  these  conditions  need  be  only  £"  in  diameter  for  the  gross 
area  is  0.60.  The  asterisks  indicate  that  rods  less  than  1"  are  not  as  a 
rule  upset.  The  asterisks  have  no  significance  when  the  table  is  used 
for  threaded  rods  not  upset.  In  order  to  obtain  the  root  area  for  any 
multiple  of  |"  between  J  and  3  it  becomes  necessary  to  use  the  following 
values  to  supplement  those  in  the  table: 


Diam.  of 
Upset 

li 

if 

2f 


Area  as 

Root  of  Thread 
0.69 
2.05 
4.62 


5.  Eye  bars  are  used  for  the  tension  members  of  pin-connected  bridges. 
The  ends  are  upset  and  punched,  as  shown  in  Fig.  40  (d),  and  then  the  holes 
are  accurately  bored  to  the  proper  size  and  at  the  proper  distance  apart. 
The  heads  are  made  the  same  thickness  as  the  rest  of  the  bar,  and  they 
are  designed  to  fully  develop  the  main  body  of  the  bar  so  that  no  bar 
tested  to  destruction  should  fail  in  the  head.  The  design  of  an  eye  bar 
is  therefore  quite  simple.  Eye  bars  are  usually  arranged  in  pairs  to  keep 
the  forces  on  the  pins  symmetrical.  The  depth  or  width  of  an  eye  bar  is 
usually  determined  by  the  size  of  other  eye  bars  and  of  other  members 


208 


PART   III  — THE   DESIGN   OF  DETAILS 


in  the  bridge.  The  thickness  of  each  bar  and  the  number  of  bars  are 
determined  by  the  required  area  of  cross  section,  which  is  found  by 
dividing  the  total  stress  by  the  unit  stress.  The  thickness  of  each  bar 
is  usually  between  1"  and  2";  2"  is  the  maximum  thickness,  while  the 
minimum  thickness  differs  with  different  widths  of  bar  and  with  different 
sizes  of  pins  as  indicated  in  the  handbooks  of  the  steel  manufacturers. 
Between  these  limits  the  thicknesses  vary  by  one-sixteenth  of  an  inch. 

1.  Riveted  Tension  Members.  —  Tension  members  other  than  rods 
and  eye  bars  are  usually  made  of  angles,  channels,  plates  and  angles, 
or  plates  and  channels.    One  or  two  angles  are  used  for  the  lighter  mem- 
bers, as  for  example,  those  in  latticed  girders  (Fig.  110),  roof  trusses  (Fig. 
116,  or  bracing  (Fig.  140).    Four  angles  are  often  used,  as  in  the  diagonal 
of  Fig.  143.     The  component  parts  of  a  member  must  be  fastened  to- 
gether to  distribute  the  stress  so  that  each  part  receives  its  share.    Two 
angles  are  fastened  at  intervals  by  stitch  rivets  (page  69:4).    Four  angles 
may  be  fastened  by  batten  plates,   by  lattice  bars,  or  by  continuous 
plates  (Fig.  125,  122,  or  126);  continuous  plates  may  be  counted  as  part 
of  the  effective  cross  section. 

2.  The  strength  of  a  tension  member  is  proportioned  to  the  least  net 
area  of  cross  section,  as  explained  on  page  206:4.    Riveted  tension  mem- 
bers are  usually  connected  to  other  members  by  means  of  connection 
plates,  and  the  least  net  areas  are  most  often  found  through  the  holes 
for  the  rivets  which  connect  the  members  to  these  plates.    The  weakest 
section  of  an  ordinary  light  tension  member  is  a  cross  section  through 
the  largest  number  of  rivet  holes.     Compare  page  209:1.    The  net  area 
of  this  section  is  found  by  combining  the  net  areas  of  the  component 
parts.     The  net  area  of  each  part  is  found  by  subtracting  the  area  of 
cross  section  of  the  holes  from  the  gross  area  found  from  the  tables.    The 
area  of  cross  section  of  a  hole  is  the  area  of  a  rectangle,  not  of  a  circle 
(Fig.  221) ;  it  is  the  product  of  the  diameter  of  the  hole  and  the  thickness 
of  metal.    The  diameter  of  the  hole  in  designing  is  taken  f"  greater  than 
the  nominal  diameter  of  the  rivet.    The  hole  is  actually  punched  only  -fa" 
larger,  but  the  metal  around  the  hole  is  damaged  during  the  process  of 
punching  so  that  it  cannot  be  counted  upon  to  carry  the  full  stress  per 
square  inch;  the  practically  universal  method  of  taking  this  into  account 
is  to  deduct  an  additional  -fa",  calling  the  hole  \"  larger  than  the  rivet. 


The  areas  of  holes  are  tabulated  on  page  303;  these  areas  may  be  used 
in  finding  the  net  areas  of  angles,  channels,  or  other  shapes.  The  net 
areas  and  the  strengths  of  tension  members  composed  of  two  angles  are 
given  on  page  327;  the  net  areas  and  strengths  of  single  angles  may  be 
found  by  dividing  these  values  by  two.  The  net  area  of  a  plate  can  be 
found  more  conveniently  by  multiplying  the  net  width  of  the  plate  by  the 
thickness,  since  both  the  area  of  the  plate  and  the  area  of  each  hole  are 
proportional  to  the  thickness.  The  table  on  page  321  is  arranged  to 
give  both  net  and  gross  areas  of  plates.  The  net  area  is  found  opposite 
the  net  width.  Thus  the  net  area  of  a  14"  plate  with  two  holes  deducted 
for  J"  rivets  is  the  same  as  the  gross  area  of  a  12^"  plate. 

3.  Illustrative  Problem. — •  Investigation.  —  Let  us  find   the  safe  load 
of  a  section  composed  of  1  PI.  12  x  |  and  4l_s4x3xf  with  holes  for 
f  "  rivets,  arranged  as  in  C  3,  Fig.  137.  Unit  stress  in  tension  =  16,000#/sq.  in. 

8.60  sq.  in.  =  4(2.48  -  f  X  f)  =  the  net  area  of  4  Ls4  x  3  x  f 
3.84  sq.  in.  =  (12  -  2  x  |)|  =  the  net  area  of  1  PI.  12  x  f 
12.44  sq.  in.  =  total  net  area 

199,000#    =  12.44  x  16,000  =  the  safe  load. 

The  net  areas  should  be  indicated  completely  as  shown  for  the  sake  of 
future  reference;  this  is  of  special  benefit  in  student  work  because  the 
instructor  can  mark  mistakes  in  such  a  manner  that  the  student  can 
tell  whether  he  took  the  wrong  number  of  holes,  the  wrong  diameter, 
or  the  wrong  thickness,  or  whether  he  took  the  wrong  value  from  the 
tables  or  made  an  arithmetical  mistake.  Thus,  in  the  first  line  are  shown 
the  number  of  angles,  the  gross  area  of  one  angle,  the  number  of  holes 
deducted  from  each  angle  (in  this  case  1),  the  diameter  of  the  hole  (f" 
larger  than  the  diameter  of  the  rivet),  the  thickness  of  the  hole  (should 
be  the  same  as  the  thickness  of  the  angles),  and  the  description  of  what 
the  result  indicates,  i.e.,  the  net  area  of  a  given  number  of  angles  of  a 
certain  size.  The  gross  area  is  taken  from  the  table  on  page  303  as 
is  also  the  area  of  one  hole,  0.33  =  f  X  f .  Similarly,  in  the  second  line 
are  shown  the  full  width  of  the  plate,  the  number  of  holes,  the  diameter 
of  each  hole,  the  thickness  of  the  plate,  and  the  description  of  the  result. 

4.  The  design  of  a  riveted  tension  member  is  an  indirect  process 
because  the  area  of  the  holes  cannot  be  found  until  the  thickness  of  the 


CHAPTER   XXXII 


THE  DESIGN   OF  TENSION  AND   COMPRESSION  MEMBERS 


209 


metal  is  known.  After  the  required  net  area  is  found,  the  size  of  the 
section  may  be  approximated  and  the  corresponding  actual  net  area 
may  be  determined;  unless  this  actual  net  area  equals  or  exceeds  the 
required  net  area  another  trial  should  be  made.  The  final  section  should 
be  the  smallest  section  which  will  satisfy  the  requirements.  The  follow- 
ing typical  problems  illustrate  the  design  of  simple  tension  members. 

First  Problem.  —  Design  a  single  angle,  with  a  row  of  |".  rivets  in  one 
leg,  to  support  a  load  of  30,000#  at  a  unit  stress  of  15,000#/sq.  in. 

2.00  sq.  in.  =  30,000  -H  15,000  =  the  net  area  required. 

The  simplest  method  is  to  use  the  table  of  net  areas  for  two  angles  (page 
327)  for  a  value  equal  to  twice  the  required  area.  With  one  hole  for 
a  J"  rivet  deducted,  the  following  sections  will  satisfy  the  requirements: 
4  x  4  x  A.  ^  X  3J  X  !,  3  x  3  x  A,  5  x  3  X  A,  4  x  3  X  f ,  3J  x  2}  X  A- 
If  the  unit  stress  were  16,000  the  problem  would  be  still  further  simplified, 
since  the  stresses  could  be  taken  directly  from  the  table  and  it  would 
be  unnecessary  to  find  the  net  area. 

Second  Problem.  —  A  hanger  is  composed  of  two  8"  channels  placed 
back  to  back  with  a  space  between  them  for  the  insertion  of  connection 
plates  at  the  ends.  They  are  riveted  to  the  plates  by  f  "  rivets  placed 
in  three  rows.  The  total  stress  is  100,000#,  and  the  unit  stress  is 
16,000#/sq.  in.  Design  the  member. 

6.25  sq.  in.  =  100,000  -^  16,000  =  the  net  area  required. 

The  gross  areas  and  web  thicknesses  of  channels  are  found  on  page 
323.  Since  the  web  thickness  is  not  a  multiple  of  -fa"  it  is  better  to 
use  the  decimal;  with  a  slide  rule  this  is  as  convenient  as  to  use  the  table 
of  areas  for  rivet  holes. 

(5.54  sq.  in.  =  2(3.35  -  3  x  |  X  .22)  =  the  net  area  of  2-8"LU  11|#) 
6.46  sq.  in.  =  2(4.04  -  3  X  |  X  .31)  =    "      "       "      "   2-8"LU  13|# 

The  result  of  the  first  trial  was  too  small,  so  the  second  trial  was  neces- 
sary. Two  8"  L2J  13|#  would  be  used.  It  is  a  good  plan  to  draw  paren- 
theses around  all  trial  designs  except  the  one  adopted. 

Third  Problem.  —  Design  a  12"  splice  plate,  with  four  lines  of  f  "  rivets, 

carry  a  stress  of  65,000#  at  16,000#/sq.  in. 


4.06  sq.  in.  =  65,000  -=-  16,000  =  the  net  area  required 

8.50  in.        =  12  -  4  x  f  =  the  net  width  of  the  plate 

\"  =  .48  =  4.06  -r-  8.50  =  the  thickness  required. 

Note  that  the  thicknesses  of  commercial  plates  vary  by  sixteenths,  and 
unless  the  resulting  thickness  is  a  multiple  of  -fa",  the  next  higher  value 
should  be  used.  The  length  of  the  splice  plate  depends  upon  the  total 
number  of  rivets  required  (page  270  :  2). 

1.  The  least  net  section  is  not  necessarily  a  right  section.  Rivets 
in  another  line  may  be  spaced  so  close  that  a  member  tested  to  destruc- 
tion would  fail  along  a  zigzag  line,  as  shown  in  Fig.  209.  The  relative 
strength  cannot  be  judged  by  comparing  the  full  net  section  along  the 
zig-zag  line  to  the  net  right  section,  because  the  unit  stress  along  the 
inclined  lines  is  not  the  same  as  along  the  transverse  lines. 
The  maximum  diagonal  tension  may  be  computed  from 
the  normal  and  the  tangential  components  of  the  longi- 
tudinal  stress.  The  minimum  stagger  which  can  be  used 
without  making  the  strength  of  the  member  less  than  at 
the  net  right  section  is  found  when  this  maximum  diagonal 
unit  stress  equals  the  unit  stress  on  the  net  right  section.  This  minimum 
stagger  may  be  found  from  the  diagram  on  page  305  for  different 
diameters  of  rivets  and  for  different  distances  between  rivet  lines.  The 
diagram  is  plotted  for  the  following  equation  : 


pjg  209. 


(2  "  d~^)  (9 


~  (d 


to 


in  which  g  =  the  gage  or  the  transverse  spacing  from  center  to  center  of 
rivets  (see  the  figure  under  the  diagram),  /  =  the  minimum  longitudinal 
pitch  or  stagger  from  center  to  center  of  rivets,  and  d  =  the  nominal 
diameter  of  the  rivets.  This  equation  is  based  upon  theory  *  which  has 
been  substantiated  by  tests  on  riveted  tension  splices,  f  If  practicable, 
the  pitch  should  not  be  less  than  the  proper  value  found  from  the  dia- 
gram. Otherwise,  a  corresponding  reduction  •  in  the  net  section  must  be 
made,  as  explained  in  the  next  paragraph.  Unfortunately,  the  importance 

*  Adapted  from  a  similar  expression  derived   by  V.  H.  Cochrane  in  the  Engineer- 
ing News,  April  23,  1908.    See  also  the  Engineering  News,  May  6,  1915. 
t  "Versuche  im  Eisenbau,"  Berlin,  1915. 


210 


PART   III— THE   DESIGN  OF  DETAILS 


of  this  requirement  is  not  yet  fully  realized  by  all  designers  and  writers 
of  specifications. 

1.  Working  Rule  for  Effective  Net  Section.  —  Obviously,  holes  that 
are  staggered  do  not  weaken  a  member  as  much  as  if  the  holes  were  all 
in  the  same  right  section.  If  a  hole  is  as  far  from  a  given  right  section 
as  the  minimum  stagger  determined  from  the  diagram  (see  preceding 
paragraph)  it  has  no  effect  upon  the  strength;  if  the  hole  is  placed  in 
the  right  section  the  net  section  is  reduced  by  the  full  area  of  the  hole; 
if  the  hole  is  between  these  limits  the  net  section  is  reduced  by  a  fraction 
of  the  area  of  the  hole.  From  the  theory  upon  which  the  formula  of  the 
preceding  paragraph  is  based  may  be  found  this  fractional  part  of  a  rivet 
hole  which  should  be  deducted  in  order  to  give  the  actual  effective  net 
section.*  This  method  is  too  cumbersome  for  general  use,  but  approxi- 
mately the  same  results  may  be  obtained  by  means  of  a  practical  working 
rule  f  which  is  recommended ;  all  variations  are  on  the  side  of  safety. 
This  rule  is  as  follows:  "  The  net  section  of  a  plate  or  shape  shall  be  defined 
as  the  least  section  obtainable  across  the  rivet  hales,  square  o_r  zigzag,  taking 
every  net  distance  in  a  diagonal  direction  at  85%  of  the  value,  except  where 
85%  of  the  distance  is  less  than  the  square  projection,  in  which  case  the  latter 
shall  be  used  instead."  The  application  of  this  rule  may  be  illustrated 
by  a  12  X  5  plate  with  holes  for  f"  rivets,  as  shown  in  Fig.  209;  the 
transverse  spacing  is  3"  with  1^"  edge  distances  and  the  longitudinal 
spacing  or  stagger  is  2".  The  net  area  of  a  right  section  is  5.00  sq.  in. 
=  (12-2xl)|;  if  the  rivets  were  placed  in  the  same  row  the  net  area 
would  become  4. 00  =(12 -4  x  1)3.  Since  the  stagger  is  less  than  the 
minimum  of  2f  found  from  the  diagram  on  page  305  (for  a  gage  of  3"), 
the  effective  net  area  must  fall  between  4.00  and  5.00  sq.  in.  The  net 
area  outside  of  the  outer  holes  is  1.00  =  2(1?  -  J)J  and  the  net  area 
between  the  inner  holes  is  1.00  =  (3  -  1)J.  The  diagonal  distance  from 
center  to  center  of  holes  is  3.60;  this  may  be  determined  graphically 
from  a  full-sized  layout,  from  the  diagram  on  page  312,  or  from 
a  table  of  squares.  Eighty-five  per  cent  of  the  corresponding  net  area 
is  1.11  =  0.85(3.60  —  1.00)|;  this  is  not  less  than  the  "  square  projec- 
tion "  1.00  =  (3  -  2)|,  so  two  such  areas  should  be  combined  with  the 

*  Derived  by  T.  A.  Smith  in  the  Engineering  News,  May  6,  1915. 

f  Developed  by  D.  B.  Steinman,  in  the  Engineering  News-Record,  June  14,  1917. 


net  areas  already  found  to  make  the  total  effective  net  area  4.22  sq.  in. 
=  2  x  1.11  +  1.00  +  1.00.  It  should  be  noted  that  the  rivet  spacing 
is  a  prerequisite  to  the  application  of  this  rule,  and  the  designer  must 
anticipate  the  details.  He  must  assume  the  number  of  rivets  in  a  right 
section  and  also  the  minimum  stagger;  these  are  sometimes  apparent, 
but  usually  he  must  either  specify  them  to  the  draftsman  or  else  indicate 
the  least  net  .area  for  which  a  member  is  designed  so  that  the  draftsman 
can  space  the  rivets  accordingly.  The  design  of  some  of  the  smaller 
members  may  be  simplified  by  considering  all  holes  in  the  same  right 
section,  unless  they  can  be  spaced  at  the  minimum  stagger  determined 
from  the  diagram;  if  only  one  or  two  additional  holes  are  involved,  par- 
ticularly if  the  stagger  is  small,  very  little  metal  is  thus  wasted. 

2.  In  the  preceding  paragraphs,  the  least  net  section  is  considered  to 
be  found  within  the  portion  of  a  member  which  is  subjected  to  the  full 
stress.  A  smaller  net  section  may  be  safely  used  near  the  ends  of  a 
member  where  part  of  the  stress  has  been  transmitted  to  the  connection 
plates  by  means  of  rivets.  In  this  way  the  size  of  the  connection  plates 
may  be  reduced.  For  illustration,  let  us  consider  the  strength  of  the 
member  LO-2  Fig.  125.  The  least  net  section  designed  to  take  the  full 
stress  is  30.12  sq.  in.  =  2(21  -  4  x  1)A  +  4(3.25  -  1  x  f)  found  through 
the  four  shop  rivets  (in  each  web)  near  the  right  end  where  the  14  x  A 
fillers  begin.  In  the  connection  at  the  left  end  of  the  member,  the  net 
area  through  the  three  field  rivet  holes  at  the  right  of  the  group  must 
be  sufficient  to  take  the  full  stress  also.  A  smaller  net  area  may  be  used 
two  spaces  to  the  left  of  this  section,  because  the  stress  has  been  reduced 
by  the  strength  of  ten  field  rivets  in  single  shear  or  60,100#  (page  310). 
Two  rivets  in  the  bottom  batten  plate  come  within  1|"  of  this  new  sec- 
tion; the  minimum  stagger  from  the  diagram  is  2J",  found  for  a  gage 
of  3f  =  2\  +  2|  -  J.  If  these  rivets  are  counted  in  the  same  right  sec- 
tion, the  net  area  is  28.00  sq.  in.  =  2(21  -  5  xl)  A  +  2(3.25  -  2  x  1  X  2) 
+  2(3.25  -  1  x  i)-  The  difference  in  strength  between  this  section  and 
the  main  section  is  only  33,900#  =  (30.12  -  28.00)16,000;  this  does 
not  exceed  60,100,  so  the  arrangement  of  rivets  is  satisfactory.  Had  this 
value  been  slightly  in  excess  of  the  strength  of  the  ten  rivets,  the  net 
area  should  be  found  more  accurately  (preceding  paragraph)  before  any 
change  were  made  in  the  arrangement  of  rivets.  In  like  manner,  the 


CHAPTER   XXXII 


THE   DESIGN   OF  TENSION  AND   COMPRESSION   MEMBERS 


211 


net  section  near  the  ends  of  a  member  may  be  reduced  by  changing 
the  rivet  stagger  instead  of  the  number  of  rivets.  The  minimum  stagger 
from  the  diagram  should  be  used  for  one  or  two  spaces  from  the  edge  of 
the  plate  where  the  stress  is  maximum  (i.e.,  towards  the  center  of  the 
member),  but  the  remaining  spaces  may  be  reduced.  As  before,  the  net 
section  at  any  point  must  be  sufficient  to  carry  that  portion  of  the  total 
stress  that  is  not  already  transmitted  by  rivets. 

COMPRESSION    MEMBERS 

1.  The  design  of  a  compression  member  is  an  indirect  process  in  which 
the  form  and  the  size  of  cross  section  are  assumed,  and  the  corresponding 
safe  load  is  compared  with  the  required  stress.     The  result  of  the  first 
trial  furnishes  a  guide  for  the  second  assumption.      The  experienced 
designer  can  usually  approximate  the  final  section  in  his  first  assump- 
tion.    Men  who  have  considerable  designing  to  do  are  equipped  with 
more  or  less  exhaustive  tables  of  safe  loads  of  members  of  different  cross 
sections  for  different  lengths.*     Tables  for  struts  composed  of  one  or 
two  angles  are  given  on  pages  330  and  331.    No  such  table  should  be 
used,  however,  until  the  underlying  principles  are  clearly  understood. 

2.  The  strength  or  safe  load  of  a  compression  member  is  found  by 
multiplying  the  unit  stress  by  the  gross  area  of  cross  section,  without 
deducting  for  holes  which  are  to  be  filled  by  rivets  (page  206:4).    The 
unit  stress  is  not  a  fixed  amount  as  for  tension  members,  but  it  varies 
with  the  length  of  a  member  and  with  the  form  and  area  of  its  cross  sec- 
tion.   A  long  member  is  more  liable  to  bend  or  buckle  than  a  short  one 
of  the  same  cross  section.    When  the  area  of  cross  section  is  distributed, 
it  is  more  effective  in  resisting  compression  than  when  the  same  amount 
of  material  is  compacted  (page  206:3).     The  unit  stress  allowed  in  the 
design  of  a  compression  member  is  determined  from  a  "  compression 
formula,"  "  column  formula,"  or  "  reduction  formula."     These  formulas 
are  of  two  general  types,  but  both  depend  upon  the  "  ratio  of  slenderness  " 

-,  in  which  I  =  the  unsupported  length  of  member  and  r  =  the  least 

*  See  also  Ketchum's  "Structural  Engineers'  Handbook,"  or  Sample's  "Properties 
of  Steel  Sections,"  McGraw-Hill  Book  Co.,  Inc.,  New  York;  also  the  handbooks  of 
the  different  steel  manufacturers. 


radius  of  gyration  (see  below),  both  in  inches.  One  type  is  the  "  straight 
line  formula,"  as  for  example  unit  stress  =  16,000  —  70-,  which  is  the 
equation  of  a  straight  line.  The  other  type  is  the  "  Rankine  (or  Gordon) 


formula,"  as  for  example,  unit  stress  = 


12,500 


1  + 


P 


-,  which  is  the  equa- 


36,000r2 

tion  of  a  curve.  Most  specifications  and  building  laws  require  the  use 
of  a  formula  of  one  of  these  types,  but  in  many  of  them  different  nu- 
merical values  are  inserted  in  place  of  the  16,000  and  the  70,  or  the  12,500 
and  the  36,000.  The  Rankine  formula  is  used  less  commonly  than 
formerly,  because  the  straight  line  formula  is  more  easily  applied  and 
gives  results  which  are  quite  as  satisfactory.  The  formula  most  com- 
monly used  is  undoubtedly  the  16,000  —  70  -,  with  a  maximum  value  of 

14,000,  which  is  recommended  by  the  American  Railway  Engineering 
Association;  this  has  been  widely  adopted.  The  unit  stresses  obtained 
from  this  formula  for  different  values  of  I  and  r  are  tabulated  on  page 
328. 

3.  The  radius  of  gyration  is  the  term  applied  to  the  expression  t/-, 

or  /  =  ar2,  in  which  a  =  the  gross  area  of  cross  section,  and  I  =  the  cor- 
responding moment  of  inertia.  The  unit  stress  for  any  compression 
member  without  intermediate  support  is  determined  by  the  least  radius 
of  gyration,  which  is  found  from  the  least  moment  of  inertia.  Because 
of  the  rectangular  construction  of  most  structural  steel  members,  the 
least  moment  of  inertia  is  found  about  one  of  two  perpendicular  axes 
(except  for  a  single  angle).  Often  the  axis  about  which  the  moment  of 
inertia  is  least  may  be  selected  by  inspection;  otherwise,  the  moments 
about  both  axes  must  be  found  and  compared.  Thus  for  example,  the 
moment  of  inertia  and  the  corresponding  radius  of  gyration  of  a  rectangle 
are  obviously  less  about  an  axis  parallel  to  the  longer  side  than  about 
an  axis  at  right  angles  to  it.  Accordingly,  a  rectangular  member  would 
buckle  first  in  a  direction  at  right  angles  to  this  axis,  as  is  apparent  from 
the  manner  in  which  an  ordinary  yardstick  bends  when  compressed. 
The  least  radius  of  gyration  of  a  single  angle  is  found  about  a  diagonal 


212 


PART  III  — THE  DESIGN  OF  DETAILS 


axis,  as  shown  in  the  tables  on  pages  325  and  326.  The  radii  of  gyration 
for  members  composed  of  two  angles  are  given  on  page  329. 

1.  The  moment  of  inertia  about  any  axis  of  a  cross  section  composed 
of  several  parts  is  found  by  combining  the  moments  of  inertia  of  the 
component  parts  about  the  same  axis,  even  though  the  parts  are  on  oppo- 
site sides  of  the  axes.  The  moment  of  inertia  Ic  of  any  component  part 
about  an  axis  through  its  own  center  of  gravity  is  found  from  a  table; 
the  moment  of  inertia  I  A  about  any  parallel  axis  AA  is  found  by  adding 
to  this  moment  of  inertia  the  product  of  the  area  of  the  compo- 
nent part  by  the  square  of  the  perpendicular  distance  between  the  axes, 
or  I  A  =  Ic  +  ax*.  The  moments  of  inertia  and  radii  of  gyration  about 
perpendicular  axes  through  their  own  centers  of  gravity  are  given  in 
the  tables  for  the  following  sections:*  I-beams,  pages  322  and  324; 
channels,  page  323;  angles,  pages  325  and  326.  The  moments  of 
inertia  of  plates  about  the  axis  perpendicular  to  the  longer  dimension 
are  given  on  page  320.  Most  of  the  values  used  in  the  design  of  simple 
steel  members  are  included  in  this  table.  Other  values  may  be  found 

bd3 
by  proportion  or  from  the  expression  -•=-,  in  which  d  is  the  dimension  at 

La 

right  angles  to  the  axis.  In  most  designs  the  moment  of  inertia  of  a  steel 
plate  about  an  axis  through  the  center  of  gravity  parallel  to  the  longer 
dimension  is  negligible,  but  when  this  moment  is  transferred  to  a  parallel 
axis,  the  product  of  the  area  by  the  square  of  the  distance  will  be  con- 
siderable. The  distances  from  the  centers  of  gravity  to  the  back  of 
channels  and  angles  are  also  given  on  the  corresponding  pages;  these 
distances  may  be  used  in  finding  the  perpendicular  distances  between 
parallel  axes.  Care  should  be  taken  to  choose  the  values  for  the  proper 
axis.  For  angles,  the  axis  parallel  to  the  longer  leg  is  marked  L-L,  while 
that  parallel  to  the  shorter  leg  is  marked  S-S.  The  diagonal  axis  about 
which  the  /  and  r  are  minimum  is  marked  M-M.  The  sub-letters  L,  S, 
and  M  are  used  to  distinguish  the  corresponding  values.  It  is  often 
most  convenient  to  find  the  moment  of  inertia  I  A  of  an  unsymmetrical 
section  about  an  axis  A  A  through  the  center  of  gravity  of  one  or  more 
of  its  component  parts  (e.g.,  the  center  of  webs),  and  then  to  transfer 

*  For  special  rolled  column  sections  in  the  form  of  the  letter  H  see  the  handbook 
of  the  Bethlehem  Steel  Company  or  the  Carnegie  Steel  Company. 


this  moment  to  a  parallel  axis  through  the  center  of  gravity  of  the  whole 
section,  by  subtracting  the  product  of  the  total  area  by  the  square  of  the 
eccentricity  (i.e.,  the  distance  between  the  two  axes),  or  Ic  =  I  A  -  «-(?• 
In  transferring  moments  of  inertia  from  one  axis  to  another  there  is  often 
some  confusion  as  to  whether  to  add  or  subtract  the  product  of  the  area 
by  the  distance  between  axes.  It  should  be  remembered  that  for  any 
given  area  the  moment  of  inertia  is  least  about  an  axis  through  the  center 
of  gravity  of  that  area.  If  this  moment  is  transferred  to  a  parallel  axis 
it  should  be  increased.  Conversely  if  the  moment  about  a  parallel  axis 
is  known,  the  moment  about  the  center  of  gravity  may  be  found  by  sub- 
traction. The  eccentricity  of  an  unsymmetrical  section  may  be  found 
by  equating  the  moments  of  areas.  If  a  thin  slice  were  cut  from  a  member 
it  could  be  balanced  on  a  thin  support  along  the  axis  CC  through  the 
center  of  gravity.  If  the  support  were  placed  along  any  other  axis  AA 
about  which  the  moment  of  inertia  I  A  is  known  and  from  which  the 
eccentricity  is  to  be  measured,  the  slice  would  tend  to  rotate  about  the 
support.  This  tendency  is  the  same  whether  the  section  is  considered 
as  a  whole  or  whether  the  component  parts  are  considered  separately. 
The  product  of  the  whole  area  by  the  eccentricity  should  equal  the  alge- 
braic sum  of  the  products  of  every  component  area  by  the  distance  from 
its  center  of  gravity  to  the  axis  A  A.  Note  that  the  moments  of  the  areas 
on  opposite  sides  of  the  axis  A  A  have  opposite  signs;  when  the  algebraic 
sum  is  zero  the  eccentricity  must  be  zero.  Some  of  the  quantities  are 
used  in  finding  both  the  eccentricity  and  the  moments  of  inertia,  and  the 
computation  may  be  simplified  accordingly. 

2.  The  forms  of  members  depend  upon  so  many  practical  considera- 
tions that  they  cannot  be  discussed  here.  Single  and  double  angles  are 
commonly  used  for  light  compression  members.  Larger  sections  are 
composed  of  channels  or  angles  with  or  without  plates.  The  component 
parts  of  any  member  must  be  held  in  the  proper  relative  position  by  stitch 
rivets,  tie  plates,  lattice  bars,  or  continuous  plates  in  order  to  properly 
distribute  the  stress.  Otherwise  each  component  part  is  free  to  buckle 
independently,  and  the  strength  of  the  member  is  no  greater  than  the 
combined  strength  of  the  component  parts  taken  singly.  The  ratio  of 
slenderness  for  any  part  of  a  member  determined  by  the  distance  between 
tie  plates  or  lattice  bars  must  not  exceed  the  ratio  of  slenderness  for  the 


CHAPTER    XXXII 


THE  DESIGN   OF  TENSION  AND  COMPRESSION  MEMBERS 


213 


entire  member  determined  by  its  full  length.  This  is  usually  provided 
for  without  special  investigation  by  the  usual  method  of  spacing  stitch 
rivets  (page  69  : 4),  or  tie  plates  and  lattice  bars  (page  70  :  1).  The 
areas  of  continuous  plates  may  be  included  in  the  effective  cross  section, 
but  tie  plates  and  lattice  bars  are  not  considered  as  part  of  the  main 
section.  The  arrangement  and  the  spacing  of  the  component  parts  of 
a  member  have  their  effect  upon  the  strength.  To  illustrate,  let  us  con- 
sider the  strength  of  two  angles  with  unequal  legs.  If  the  member 
receives  no  intermediate  support,  the  longer  legs  of  the  angles  are  placed 
together.  This  arrangement  gives  better  distribution  of  metal  because 
the  radii  of  gyration  about  perpendicular  axes  are  kept  more  nearly 
equal,  and  the  least  radius  is  larger  than  if  the  angles  were  placed  with 
their  shorter  legs  together.  This  is  the  usual  arrangement  for  struts, 
bracing,  and  web  members  of  latticed  girders  and  roof  trusses.  In  de- 
termining the  strength  of  a  member  with  intermediate  support,  such  as 
a  chord  member  of  a  latticed  girder  or  light  roof  truss  which  is  supported 
by  web  members,  there  are  two  different  lengths  to  be  considered.  The 

unit  stress  is  found  from  the  greatest  ratio  of  slenderness  -,  and  not  neces- 

r 

sarily  from  the  least  radius  of  gyration.  Since  the  length  between  lateral 
supports  is  usually  greater  than  between  panel  points,  the  corresponding 
radius  of  gyration  should  also  be  greater  in  order  to  keep  the  ratios  of 
slenderness  more  nearly  equal,  or  at  least  so  that  the  larger  ratio  is  mini- 
mum. The  angles  of  such  members  are  thus  usually  placed  with  their 
shorter  legs  together.  Each  member  should  be  analyzed  in  this  manner. 
Certain  practical  limitations  are  often  specified  for  the  thicknesses  of 
different  component  parts  of  compression  members.  Common  examples 
are  (a)  that  the  thickness  of  web  plates  must  not  be  less  than  -fa  the  dis- 
tance between  the  lines  of  rivets  which  connect  the  plates  to  the 
angles;  (6)  that  the  thickness  of  cover  plates  must  not  be  less  than  TV 
the  distance  between  the  lines  of  rivets  which  connect  them  to  the 
angles  or  channels ;  and  (c)  that  the  thickness  of  the  angles  without 
cover  plates  must  not  be  less  than  TV  of  the  outstanding  leg  of  one 
angle.  • 

1.   The  following  typical  problems  illustrate  the  design  or  the  investiga- 
tion of  some  of  the  more  common  compression  members. 


First  Problem.  —  Design  a  single  strut  10  feet  long  to  carry  a  stress  of 


50,000#  at  a  unit  stress  of  16,000  -  70  -. 


The  table  of  safe  loads  on 


page  330  is  based  upon  this  unit  stress,  so  it  may  be  used  directly. 
Under  the  column  headed  10  feet  is  found  the  stress  51,000  opposite  a 
6x6xJ,  which  would  be  used.  If  such  a  table  were  not  available,  a 
table  of  properties  of  angles  (page  325)  must  be  used.  Unless  the 
designer  is  guided  by  experience  or  otherwise,  he  must  assume  a  section 
and  then  investigate  it.  He  may  approximate  the  section  roughly  by 
dividing  the  given  stress  by  a  unit  stress  of  10,000#/sq.  in.  In  this  prob- 
lem the  required  area  is  approximately  5  sq.  in.,  so  a  6  x-6  x  T7ff  is  investi- 
gated. The  least  radius  of  gyration  of  a  single  angle  about  a  diagonal 

70  x  10  x  12 


axis  is  1 . 19  in.    The  unit  stress  is  8,940#/sq.  in.  =  16,000  - 


1.19 


which  multiplied  by  the  area  5.06  sq.  in.  gives  a  safe  load  of  45,200#. 
This  is  too  small,  so  the  next  larger  size  is  tried  in  a  similar  manner  and 
found  sufficient,  the  safe  load  being  51,100#. 
Second  Problem.  —  Find  the  thickness  of  two  5  X  3§  angles  to  carry 

a  stress  of  75,000#  at  16,000  -  70  -  pounds  per  square  inch.    The  angles 

are  11  feet  long  and  connect  to  a  \"  gusset  plate  placed  between  them. 
If  no  other  member  is  connected  to  this  member  in  such  a  way  as  to  give 
intermediate  support  to  prevent  its  buckling  in  one  direction,  the  longer 
legs  of  the  angles  will  be  connected  to  the  plate  and  hence  be  parallel 
and  2"  apart.  The  radii  of  gyration  about  both  axes  appear  in  the  middle 
table  on  page  329.  The  approximate  area  of  two  angles  is  7.5  sq.  in. 
=  75,000  -f-  10,000.  From  the  areas  of  two  angles  in  the  above  table 
this  falls  between  -f$  and  \  inch  in  thickness.  The  latter  would  have  a 

safe   load   of  80,000#  =  8.00  (l6,000  -  —  X^^  12Y  the  former  only 


70,000#,  hence  2  Ls  5  x  3?  x  2  would  be  used.  If  the  angles  were  f " 
apart  the  safe  load  could  be  taken  directly  from  the  table  on  page  331. 
If  neither  of  these  tables  were  available  the  radii  of  gyration  would  have 
to  be  found  from  the  properties  of  angles  (page  325).  The  radius 
about  an  axis  parallel  to  the  shorter  legs  is  the  same  for  one  or  two 
angles  because  the  axis  through  the  center  of  gravity  of  the  member 


214 


PART   III  — THE   DESIGN   OF   DETAILS 


passes  through  the  centers  of  gravity  of  each  angle;  thus  both  the  mo- 
ment of  inertia  and  the  area  are  doubled  and  the  radius  remains  un- 
changed. The  moment  of  inertia  about  the  other  axis  is  18.90  in4 
=  2[4.05  +  4.00(0.25  +  0.91)2]  and  the  corresponding  radius  is  1.54  in. 
=  V18.90-H  (2  X  4.00). 

Third  Problem.  —  Find  the  safe  load   of  a  20-foot  column  composed 
of  two  12  x  J  plates  and  two  10"  L2J  15#,  6"  back  to  back,  as 

12,500 


Fourth  Problem. —  Find  the  least  radius  of  gyration  for  a  top-chord 
section  composed  of  2  web  plates  18 x  5,  1  cover  plate  21  X  3,  two  top 
angles  3  x  3  x  f ,  and  2  bottom  angles  4  x  3x  5, 
arranged  as   shown   in   Fig.  214  (6).     It  is   con- 
venient to  select  all  the  necessary  areas,  moments 
of  inertia,  and  distances  to  centers  of  gravity  from 
the  tables  at  the  outset.     The  distances  may  be 
recorded  directly  upon  the  sketch. 


shown  in  Fig.  214  (a).    The  allowed  unit  stress  =• 


1  + 


6.00  sq.  in. 
page  321) 
72.0    in4        =  / 

4 . 46  sq.  in.  =  area 
66.9    in4        =  I 

2.3    in4 


36,000r2 
area  of  one  12  x  |  (by  inspection,  or  from 


12  x  £  (page  320) 

10"LJ15# 

10"  U  15#  about  axis  AA 

10"LJ15#      "        "    BE 


0.64  in.        =  dist.  from  b.  of  web  to  c.  of  g. 

133.8  =  2  x  66.9  =  7  of  2  LU  about  AA 

330.7  =  2  x  6.00(5.00  +  0.25)2  =  7  of  2  Pis.  about  A  A  (neglecting 

the  7  about  axis  through  c.  of  g.  of  PL) 
464.5  =  total  7  about  AA 

122.8  =  2(2.3  +  4.46  x  3.642)  =  7  of  2  U>J  about  BB 
144.0  =  2  x  72.0  =  7  of  2  Pis.  about  BB 

266.8  =  total  7  about  BB 

12.7  in2  =  266.8  -s-  2(6.00  +  4.46)  =  the  least  r2 
20.92  x  12,500 


A-    - 

J&.J&L 

~"  C 

Fig.  214  (b). 

gh  its  c.  of  g. 

through  its  c.  of  g. 

(i        tt  ft  tt  it 

tt        a  tt  tt  tt 
tt        ti  tt  tt  tt 

,     Ir-i.            1U.OU                  —                                     Zl  X  2 
3  ,£,64 

Fig.  2 
323) 

,2             2.11     "  "   =     "    "     "      L  3  x3  x  f 

14  (a).          3.25      "   "    =      "      "     "      "4x3X5 
1.8      in4      =7     "     "     "  3  x3x|  about  axis  t'hrou 
2.4      "        =     "     "     "     "   4x3xJ      "     hor.  axis 
5.0      "         =     "     "     "     "   4x3x|      "     vert.    " 
243.0      "         =     "     "     "    PI.  18  xi      "     hor.     " 

385.9      "         =     "     "     "     "   21  x  i       "     vert.    " 

232,000#  = 


1  + 


(20  x  12)2 
36,000  x  12.7 


the  total  safe  load. 


Note  that  when  the  compression  formula  contains  r2  it  is  unnecessary 
to  find  r. 


39.22sq.  in.  =  2(9.00  +  2.11  +3.25)  +  10.50  =  total  area 
I 

99.8  in3   =  10.50  x  (9.25  +  0.25)  =  moment  of  cover  plate 

35.3  "    =2x2.11x8.36=  "  2  top  Ls 
135.1    "    =  sum 

54.7    "    =2x3.25x8.42=  "  2  bottom  Ls 

80.4  "    =  algebraic  sum  of  moments  about  centers  of  webs. 
2. 05 in.  =  80.4  -r-  39.2  =  e  =  eccentricity. 

486  in4  =  2  x  243 . 0  =  7  of  webs  about  centers  of  webs 

948  "  =  10. 50x9. SO2  or  99.8  X  9.50  =  7  of  cover  plate 

295  "  =  2(1. 8 +  2. 11x8. 362)  or  3. 6 +35.3  X  8. 36  =  7  of  top  Ls 

461  "  =2(2.4  +  3.25  X  8.422)  or  4.8  +  54.7  x  8.42  =  7  of  bottom  Ls 

2190  "  =  total  7  about  axis  through  centers  of  webs. 

165  "  =39.22  x  2. 052  or  80.4  x  2. 05 

2205  "  =  total  7  about  horizontal  axis  through  c.  of  g. 


CHAPTER   XXXII 


THE  DESIGN   OF  TENSION  AND  COMPRESSION   MEMBERS 


215 


386  in4   =  7  of  cover  plate  about  vertical  axis 
882    "    =  2  x  9.00  X  (6.75 +  0.25)2  =  7  of  webs 
283    "    =  2(1.8  +2.11  x  8.142)  =  7  of  top  Ls 
483    "    =  2(2.4  +  3.25  x  8.582)  =  /  of  bottom  Ls 
2034    "    =  total  7  about  vertical  axis  through  c.  of  g. 
7.2 in.  =  V2025  -s-  39.2  =  least  radius  of  gyration. 

The  table  of  squares  (page  332)  may  be  used  to  advantage  in  a 
problem  which  involves  squares  or  square  roots. 

MEMBERS   WHICH  RESIST  BENDING  AND   DIRECT  STRESS 

1.  Tension  or  compression  members,  such  as  the  top  or  bottom  chords 
of  roof  trusses  or  the  end  posts  of  bridge  trusses,  are  sometimes  subjected 
to  transverse  bending  as  well  as  direct  axial  stresses.  They  must  be 
designed  so  that  the  combined  stresses  on  the  extreme  fibers  do  not  exceed 
the  allowed  unit  stresses  determined  from  the  compression  formulas.* 
The  unit  stress  in  direct  tension  is  found  by  dividing  the  total  tensile 
stress  by  the  net  area  of  cross  section.  The  unit  stress  in  direct  com- 
pression is  found  by  dividing  the  total  compressive  stress  by  the  gross 
area  of  cross  section.  These  areas  should  be  taken  near  the  point  of 
maximum  bending.  The  unit  stress  in  the  extreme  fiber  due  to  bending 

is  found  by  equating  the  bending  moment  to  the  resisting  moment  — 

C 

and  solving  for  /.  In  an  unsymmetrical  member  the  value  c  in  a  tension 
member  should  be  taken  from  the  neutral  axis  to  the  extreme  fiber  in 
tension,  while  in  a  compression  member  it  should  be  taken  from  the 
neutral  axis  to  the  extreme  fiber  in  compression.  Two  allowed  unit 
stresses  should  be  considered,  one  with  the  radius  of  gyration  about  an 
axis  perpendicular  to  the  direction  of  bending,  the  other  with  the  radius 
about  an  axis  parallel  to  the  direction  of  bending.  The  former  should 
mot  be  exceeded  by  the  combined  unit  stresses  due  to  bending  and  direct 

*  Some  designers  use  different  unit  stresses  for  bending  and  for  direct  stress  and 
Combine  the  resulting  areas;  see  Johnson-Bryan-Turneaure's  "Framed  Structures," 
Vol.  Ill,  John  Wiley  and  Sons,  Inc.,  New  York. 


stress,  but  the  latter  should  not  be  exceeded  by  the  direct  unit  stress 
alone. 

Illustrative  Problem.  —  Design  a  horizontal  compression  member 
8  feet  long  which  will  support  a  load  of  2000#  at  its  center.  The  direct 
compression  is  75.000#  and  the  member  is  composed  of  two  6x4  angles, 


"  b.  to  b.   4000#  ft. 


2000 


X  4  =  MB. 


Assume  2  Ls  6  x  4  x  \,  area  =  9.50,  distance  from  center  of  gravity 
to  back  of  shorter  leg  =  distance  from  neutral  axis  to  extreme  fiber  in 
compression  =  c  =  1 . 99,  7  =  34 . 8,  and  r  =  1.91  about  the  axis  per- 
pendicular to  the  direction  of  bending. 

7,900#/sq.  in.  =  75,000  ^-  9.50  =  direct  unit  stress 
4000  x  12  x  1.99 


2,740 


34.8 


=  unit  stress  due  to  bending 


10,640     "    "    =  total  unit  stress 
12,480     "    "    =  16,000  -  7°  *  8*  12 


allowed  unit  stress  which  is  con- 


siderably  greater  than  10,640. 

Assume  2  Ls  6  x  4  x  A,  area  =  8.36,  c  =  1.96,  7  =  31.0,  r  =  1.92 
8,970#/sq.  in.  =  75,000  +  8.36  =  direct  unit  stress 
4000  x  12  x  1.96 


tl     it        if 


3,040 
12,010 
12,500  "  "  "  =  16,000  - 


12,000 


31.0 
"  "     "    =  total  unit  stress 

70  x  8  X  12 

1.92 
70  x  8  x  12 


=  unit  stress  due  to  bending 


"    =  16,000  - 


1.68 
pression  alone. 


=  allowed  unit  stress 

=  allowed    unit    stress    for    com- 


Since  12,010  is  reasonably  close  to  12,500  (f"  angles  would  be  too 
small)  and  since  8,970  does  not  exceed  12,000,  2  Ls6  x  4  x  TV  would 
be  used. 


216 


PART  III  — THE  DESIGN  OF  DETAILS 


LATTICE  BARS  AND  TIE  PLATES 


1.  The  design  of  lattice  bars  and  tie  plates  or  batten  plates  for  com- 
pression  members    cannot   be   theoretically   developed.      Certain   mini- 
mum sizes  based  upon  the  experience  of  many  years  are  demanded  by 
the  specifications  in  common  use.     These  requirements  often  determine 
the  sizes  to  be  used,  but  the  lattice  bars  must  also  be  large  enough  to 
carry  the  stresses  found  by  the  method  explained  below.     This  method 
of  design  gives  safe  results  for  all  members  except  those  of  very  large 
structures  which  should  receive  more  careful  consideration.     Some  recent 
column  tests  seem  to  indicate  that  this  method  results  in  lattice  bars 
about  twice  as  strong  as  necessary. 

2.  A  tie  plate  should  be  placed  in  the  plane  of  every  system  of  lattice 
bars  as  near  each  end  of  the  member  as  possible,  and  wherever  the 
lattice  system  is   interrupted.     The   plates  at  the  ends  should  extend 
longitudinally  at  least  as  far  as  the   transverse  distance  between  the 
lines  of  rivets  which  attach  them  to  the  member.     Intermediate  plates 
need   be  only  one-half  as  large.      The  rivets  in  tie  plates  are  usually 
spaced   about  3"   apart.      The  thickness  of  tie   plates  should  not  be 
less  than's3^  of  the  distance  between  the  rivet  lines  mentioned   above. 
A   plate  provided  for  another  purpose  may  serve  also  as  a  tie   plate 
even   though   it   is  not  placed  in  position  before  erection.    Tie  plates 
with   or  without    lattice   bars  are   used   on    tension   members   to   dis- 
tribute the  stresses,  although  they  do  not  need  to  be  designed  to  resist 
buckling. 

3.  The  minimum  widths  of  lattice  bars  are  commonly  specified  as 
follows:    2§"  for  f"  rivets,  2\"  for  f"  rivets,  and  2"  for  f"  rivets,     f" 
rivets  are  used  for  latticing  flanges  3J"  wide  or  over.    One  rivet  is  gener- 
ally used  at  each  end  unless  the  flanges  exceed  5"  in  width,  when  two  are 
used.    Double  lattice  bars  are  used  when  the  transverse  distance  between 
rivet  lines  exceeds  1'  3".    The  minimum  thickness  of  single  lattice  bars 
is   -fa  of    the    length    from   center  to   center   of  end    holes;    similarly 
the  minimum  thickness  of  double  lattice  bars  is  -fa  of  the  same  length. 
The  table    on    page    315   shows    the    maximum    lengths   for    different 
thicknesses    for    these    ratios    and    for    others    which    are    sometimes 
specified. 

-V 


4.  Method  of  Design.  —  Compression  members  which  are  designed 
for  a  unit  stress  of  16,000  —  70  -  could  be  designed  for  16,000  the  same 
as  a  tension  member  were  it  not  for  the  tendency  to  buckle.  It  may  be 

reasoned  that  the  term  70  -  represents  the  stress  in  the  extreme  fiber 

r 

due  to  this  tendency  to  buckle.  It  may  fairly  be  assumed  that  in  effect 
this  is  equivalent  to  the  fiber  stress  caused  by  transverse  bending  forces 
uniformly  distributed,  the  member  acting  as  a  beam.  The  corresponding 
shearing  stresses  are  taken  either  by  continuous  plates  (as  in  a  beam  or 
girder)  or  by  lattice  bars  (as  the  diagonals  in  a  latticed  girder).  The 
stress  in  each  bar  may  be  found  accordingly  as  follows: 


MB  =~^ — (page  188  :2);  if  we  let  R  =  -  -  =  the  reaction   or  maxi- 

D 

RL  Rl 


mum  shear  we  have  MB  =  —r-  whence 


Also  /  =  ar2  (page  211:3),  and  /  =  70  -  (from  above). 

Substituting  these  values  in  ma  =—  (page  199:2),  we  have  R  =  -     —  , 

c  c 

in  which  a  =  the  total  area  of  cross  section,  r  =  the  radius  of  gyration 
about  an  axis  perpendicular  to  the  plane  of  the  lattice  bars,  and  c  =  the 
distance  from  this  neutral  axis  to  the  extreme  fiber.  This  shear  is  the 
transverse  component  of  the  stress  in  the  lattice  bar  and  from  it  the  stress 
can  be  determined  by  multiplying  by  the  cosecant  of  the  angle  which  the 
lattice  bar  makes  with  the  longitudinal  axis  of  the  member.  If  this  angle 

is  45°,  the  stress  in  the  bar  is  -  .    If  a  member  is  latticed  in  two  planes. 

c 

the  bars  in  each  plane  are  stressed  only  one  half  the  above  amount 
Similarly,  if  a  continuous  plate  is  used  on  one  side  and  lattice  bars  on  th( 
other  as  in  chord  members,  the  plate  and  the  system  of  bars  may  each  be 
considered  to  take  one-half.  Since  lattice  bars  resist  both  tension  anc 
compression  they  must  be  strong  enough  for  either.  They  are  designec 

for  compression  at  16,000  -  70  -,  for  this  determines  the  size. 


CHAPTER   XXXII 


THE  DESIGN  OF  TENSION  AND  COMPRESSION   MEMBERS 


217 


Illustrative  Problem.  —  Design  the  lattice  bars  for  the  top-chord  sec- 
tion of  the  fourth  problem  on  page  214.  Since  a  cover  plate  is  used 
on  top,  the  bottom  lattice  bars  need  be  designed  for  only  half  the  bend- 
ing. From  Fig.  214  (6)  the  distance  between  rivet  lines  is  obviously  more 
than  1'  3",  so  double  latticing  is  required,  and  therefore  the  angle  of 

inclination  is  45°.     The  maximum  stress  in  one  bar  is  =  x  5  X  -      -in 


which  a  =  39.2,  r  =  7.2  = 


,,andc  =  11.25  =  6.75  +  0.50  +  4.00. 


Substituting  these  values  and  solving,   we  find  the  stress  in  one  bar 


=  2480#.  |"  rivets  should  be  used  since  the  4"  angle  exceeds  3£",  and 
bars  at  least  2\"  wide  must  be  used.  The  length  of  each  bar  from  center 
to  center  of  end  rivets  is  28"  =  1.41  X  2(6.75  +  0.50  +  2.50),  and 
the  minimum  thickness  is  \  =  ff .  The  area  of  a  2\  x  \  is  1 . 25,  and 

the   radius   of   gyration   is   0.14  = 


2.5x0.5" 


12x2.5x0.5 


,  whence  the  safe 


load   is   2500#  =  1.25  (l6,000-?^|^.      This    is    greater    than    the 
required  stress  2480,  so  the  bars  are  satisfactory. 


V 


CHAPTER  XXXIII 
THE  DESIGN  OF  PLATE  GIRDERS 

SYNOPSIS:  Three  methods  of  designing  the  main  cross  section  of  a  girder  are  pre- 
sented and  compared.  The  discussion  of  details,  such  as  the  lengths  of  cover  plates, 
the  spacing  of  flange  rivets,  and  the  sizes  of  stiffening  angles  and  splices  is  left  for 
subsequent  chapters. 


1.  Plate  girders  are  designed  to  meet  a  great  variety  of  conditions, 
as  explained  on  page  95  : 1.     The  common  forms  of  cross  section  are 
shown  in  Fig.  95,  the  majority  of  girders  being  of  one  of  the  first  two 
forms.     In  order  to  simplify  the  phraseology,  most  of  this  chapter  has 
been  written  to  apply  to  horizontal  girders  with  vertical  loads,  each 
flange  being  composed  of  two  angles,  with  or  without  cover  plates. 

2.  Analysis  of  Forces.  —  The  external  forces  which  act  upon  a  plate 
girder  must  satisfy  the  three  equations  of  equilibrium   (page  183:2). 
If  the  girder  is  cut  by  an  imaginary  plane,  the  external  forces  which  act 
on  either  segment  are  not  in  equilibrium  by  themselves,  but  they  are 
held  in  equilibrium  by  the  internal  forces  or  "  stresses  "  acting  in  the 
fibers  which  are  cut  by  the  section  plane.    The  vertical  components  of 
these  forces  are  shearing  stresses;   these  are  resisted  by  the  web,  as  dis- 
cussed in  Chapters  XXXIX  and  XL,  pages  266  and  270.    The  hori- 
zontal components  of  these  internal  forces  must  satisfy  the  H  equation 
of  equilibrium  provided  the  external  forces  are  all  vertical;    thus  the 
sum  of  all  tensile  stresses  (which  tend  to  elongate  the  girder)  must  equal 
the  sum  of  all  compressive  stresses  (which  tend  to  shorten  the  girder) 
as  in  a  beam.    The  sum  of  the  moments  of  the  external  forces  which  act 
on  the  segment  is  the  bending  moment,  and  the  sum  of  the  moments 
of  the  internal  forces  cut  by  the  section  plane  is  the  resisting  moment; 
these  two  moments  must  be  equal  in  order  to  satisfy  the  M  equation  of 
equilibrium.     If  the  point  of  moments  is  taken  in  the  section  plane  the 
moment  of  the  vertical  components  of  the  internal  forces  is  zero,  and 


only  the  horizontal  components  need  be  considered.  The  section  pli 
is  taken  at  the  point  of  maximum  bending  moment  and  the  girder  is 
designed  to  furnish  the  proper  resisting  moment  by  one  of  the  methods 
described  in  this  chapter. 

3.  The  depth  of  a  plate  girder  is  often  predetermined  by  specific  re- 
quirements.    Within  practical  limits,  flanges  may  be  designed  for  any 
depth  of  girder;    as  the  depth  is  increased  the  flanges  become  lighter, 
and  conversely.     The  most  economical  depth  is  from  one-seventh  of 
the  length  for  short  spans  to  one-twelfth  the  length  for  long  spans;   in 
the  absence  of  other  data  an  average  value  of  one-tenth  the  length  may 
be  chosen;   the  maximum  depth  is  limited  to  about  10'-6"  by  the  over- 
head clearance  available  during  shipment.     The  depth  of  the  web  plate 
is  usually  made  a  multiple  of  2",  and  preferably  a  multiple  of  6";   the 
depth  from  back  to  back  of  flange  angles  is  usually  \"  or  \"  greater 
than  the  depth  of  the  web  (page  95  : 3). 

4.  The  thickness  of  the  web  plate  must  be  such  that  the  strength  of  the 
web  is  sufficient  to  transmit  the  shearing  stresses,  as  explained  on  page 
266: 3.    The  web  plate  must  also  be  thick  enough  to  furnish  proper  bearing 
for  the  flange  rivets,  as  explained  on  page  255 : 2.     The  usual  values  are 
from  -fa"  to  f"  (page  266: 3)  with  a  minimum  value  equal  to  ^^  of  the  ver- 
tical clear  distance  between  flange  angles.    Usually  a  value  is  assumed  with 
due  regard  to  this  minimum,  then  the  flanges  of  the  girder  are  designed, 
and  finally  the  strength'  of  the  web  plate  is  investigated.     If  necessary, 
these  steps  may  be  repeated  until  a  satisfactory  solution  is  obtained. 


.218 


CHAPTER   XXXIII 


THE   DESIGN  OF  PLATE  GIRDERS 


219 


1.  The  flanges  of  comparatively  light  girders  are  composed  of  two 
angles  each.     Cover  plates  are  added  to  the  flanges  of  heavier  girders 
to  provide  additional  flange  area  where  needed;   the  cover  plates,  unlike 
the  angles,  need  not  extend  the  full  length  of  the  girder,  but  they  may 
be  cut  off  at  points  beyond  which  the  remaining  area  is  sufficient  to  carry 
the  reduced  flange  stress,  as  explained  in  Chapter  XXXVIII,  page  259. 
It  is  not  practical  to  use  cover  plates  unless  the  outstanding  legs  of  the 
flange  angles  are  at  least  5  or  6  inches;   the  cost  of  using  heavier  angles 
would  be  less  than  the  cost  of  using  cover  plates  on  account  of  the  extra 
punching  and  riveting.    Additional  angles  or  vertical  plates  may  be  used 
in  the  heavier  girders,  as  shown  in  Fig.  95,  c,  d. 

2.  Flange  angles  with  unequal  legs  should  be  used  whenever  prac- 
ticable; angles  with  equal  legs  less  than  6  inches  are  seldom  used.    6x6 
angles  are  used  when  6  x  4  x  f  angles  are  not  large  enough,  or  when  the 
flange  rivets  in  the  web  legs  must  be  staggered  to  meet  the  requirements 
of  Chapter  XXXVII,    page   241.     8x8   angles   are  reserved  for  very 
heavy  girders;    they  are  not  used  without  cover  plates.    When  unequal 
legs  are  used,  the  shorter  leg  is  riveted  to  the  web  plate  and  the  longer 
leg  is  outstanding.     In  this  position  the  center  of  gravity  of  the  flange 
is  nearer  the  back  of  the  angle  and  hence  farther  from  the  neutral  axis; 
the  resisting  moment  is  thus  made  correspondingly  greater  (why?).    The 
lateral  stiffness  is  also  increased  by  placing  the  longer  legs  horizontally. 

3.  The  cover  plates  are  made  wide  enough  to  fully  cover  the  angle; 
plates   of   commercial   widths   will   usually   project   beyond   the  angles. 
18"  plates  (or  17)  are  used  with  8"  angles,  14"  plates  (or  13)  with  6" 
angles,  and  12"  (or  11)  plates  with  5"  angles.     It  is  convenient  to  find 
the  total  thickness  of  cover  plates  as  if  there  were  only  one  plate  on  each 
flange;    this  total  thickness  may  then  be  subdivided  into  the  proper 
number  of  plates.    No  plate  should  be  thicker  than  f "  nor  less  than  the 
minimum  thickness  of  metal  allowed  (usually  f").     Usually  the  number 
of  plates  used  is  the  smallest  which  will  meet  these  requirements  so  that 
the  cost  of  handling  and  punching  extra  plates  may  be  saved.    Full-sized 
holes  cannot  be  punched  satisfactorily  in  metal  thicker  than  f";    they 
must  be  either  drilled  or  sub-punched  and  reamed  (page  30  : 2).     The 
cover  plates  should  be  made  approximately  of  equal  thickness,  but  they 
may  differ  by  Ty  when  the  total  thickness  is  not  an  exact  multiple 


of  the  number  of  plates.  When  plates  of  different  thickness  are  used, 
the  thicker  plates  should  be  nearer  the  angles. 

4.  Distribution  of  Area.  —  The  net  of  the  flange  angles  should  prefer- 
ably be  as  large  as  the  net  area  of  the  cover  plates.    In  other  words,  the 
net  area  of  the  angles  should  be  50%  of  the  area  which  remains  after 
the  portion  (if  any)  of  the  web  plate  counted  as  flange  area  is  deducted 
from  the  total  net  area  required.     This  requirement  is  often  specified 
in  order  to  overcome  the  tendency  of  a  few  designers  to  put  considerably 
more  than  50%  of  the  area  into  the  cover  plates  to  save  metal;    this 
tendency  might  result  in  angles  which  are  too  weak  to  transmit  the  cor- 
responding stress  from  the  web  plate  to  the  cover  plates. 

The  author  has  seen  recently  a  flagrant  violation  of  this  specification  in  an 
existing  main-line  railroad  bridge  in  which  cover  plates  about  6"  thick  are  connected 
to  the  web  by  6  X  3i  X  ^  flange  angles. 

In  some  of  the  very  heavy  girders  it  is  impossible  to  obtain  angles 
which  are  large  enough  to  furnish  50%  of  the  area  mentioned,  but  the 
specifications  provide  for  this  contingency  by  allowing  "  the  largest  size 
of  angle  "  to  be  used.  In  case  no  clause  appears  in  the  adopted  specifica- 
tions *  regarding  the  relative  distribution  of  area,  it  is  the  common  prac- 
tice to  make  the  area  of  the  angles  50  %  of  the  net  area  remaining  after 
I  (or  other  portion)  of  the  area  of  the  web  plate  is  deducted,  provided 
the  angles  are  no  thicker  than  J".  Thus,  6  X  6  X  f  angles  are  often  used 
even  though  the  cover  plates  are  of  somewhat  greater  area;  this  is  done 
so  that  the  rivet  holes  in  the  angles  may  be  punched  (see  preceding 
paragraph) . 

5.  The  Compression  Flange.  —  It  is  desirable  from  the  standpoint 
of  fabrication  to  make  both  flanges  of  a  plate  girder  alike.     Unless  the 
top  flange  is  braced  transversely  to  prevent  buckling  it  may  have  to 
be  made  of  a  different  cross  section.     The  flange  stress  is  the  same  in 
the  compression  flange  as  it  is  in  the  tension  flange  as  will  be  seen  later 
(page  221  :2).     The  allowed  unit  stress  is  less  in  compression  than  in 
tension,  but  the  effective  area  is  greater  because  no  deduction  need  be 
made  for  rivet  holes.     The  tension  flange  is  usually  designed,  and  the 

*  For  example,  the  "Specifications  for  Steel  Railway  Bridges,"  of  the  American 
Railway  Engineering  Association,  Chicago. 


220 


PART   III  — THE   DESIGN   OF  DETAILS 


compression  flange  is  made  like  it  unless  the  compression  flange  is  found 
not  to  have  the  proper  lateral  stiffness;  the  compression  flange  should 
never  be  made  of  smaller  gross  area  than  the  tension  flange.  The  com- 
pression flanges  of  bridge  girders  are  usually  braced  at  intervals  either 
by  lateral  bracing  (Fig.  142)  or  by  gussets  at  the  floor  beam  connections 
(Fig.  99);  in  the  majority  of  cases  the  two  flanges  may  be  made  alike. 
The  compression  flanges  of  crane-runway  girders  are  sometimes  latticed 
to  other  girders  (page  112:6),  in  which  case  the  flanges  may  be  made 
alike;  otherwise  the  top  flange  must  often  be  made  heavier  or  wider, 
as  shown  in  Fig.  95  (e)  and  (/).  After  the  tension  flange  of  a  girder  is 
designed,  the  strength  of  a  like  compression  flange  should  be  investigated. 
The  allowed  unit  stress  is  based  upon  the  ratio  of  the  width  of  the  flange 
to  the  unsupported  length.  The  specifications  recommended  by  the 
American  Railway  Engineering  Association  state  that  the  unit  stress 
per  square  inch  of  gross  area  of  the  compression  flange  must  not  exceed 

16,000  -  200  7  when  angles  alone  or  angles  with  cover  plates  are  used,  or 

16,000  -  150  r  when  angles  with  channel  covers  are  used;  b  =  the  extreme 

width  of  flange  in  inches,  and  I  =  the  distance  in  inches  between  lateral 
supports.  If  the  compression  flange  is  not  braced,  I  =  the  full  length 
of  the  girder.  The  thickness  of  flange  angles  used  without  cover  plates 
should  not  be  less  than  one-twelfth  the  length  of  each  outstanding 
leg. 

1.  Three  Methods  of  Design.  —  The  flanges  of  a  plate  girder  may  be 
designed  by  any  one  of  three  methods,  viz.:  Case  A,  in  which  the  flange 
angles  and  cover  plates  are  assumed  to  resist  the  entire  flange  stress  due 
to  bending  moment;  Case  B,  in  which  the  resisting  moment  of  the  web 
plate  is  considered;  and  Case  C,  in  which  the  moment  of  inertia  of  the 
net  cross  section  is  used  in  much  the  same  manner  as  in  the  design  of 
beams.  The  method  of  Case  C  is  given  as  an  alternate  method  in  the 
more  modern  specifications,  but  it  is  not  recommended  for  general  use 
on  account  of  the  somewhat  indirect  and  laborious  calculation  involved. 
It  is  practical  only  when  exhaustive  tables  are  accessible,  which  give  the 
moments  of  inertia  or  the  section  moduli  of  all  types  and  sizes  of  girders, 
for  different  sizes  of  rivet  holes.  This  method  is  an  application  of  the 


general  formula  for  flexure,  mB  =  —    (page    199  : 2)   in  which    /  =  the 

moment  of  inertia  of  the  net  cross  section.  Theoretically  the  neutral 
axis  is  not  at  the  center  of  the  web  because  the  tension  half  of  the  girder 
is  weakened  by  the  rivet  holes,  while  the  compression  half  is  not.  This 
refinement  is  not  adopted  ordinarily,  but  for  convenience  the  upper  half 
is  considered  like  the  lower  half;  that  is,  the  moments  of  inertia  of  the 
holes  in  both  flanges  and  in  the  whole  web  are  deducted  from  the  moment 
of  inertia  of  the  cross  section  (page  212  : 1).  The  method  of  Case  B  is 
meeting  with  most  favor  at  the  present  time,  and  has  been  adopted  quite 
generally.  The  results  are  obtained  more  readily  by  means  of  this 
method  than  by  the  more  precise  method  of  Case  C,  and  they  are  very 
nearly  the  same.  The  assumption  is  made  that  the  flange  stress  is  uni- 
formly distributed  throughout  the  whole  flange,  the  resultant  acting 
at  the  center  of  gravity  of  the  flange.  The  effective  depth  is  therefore 
the  distance  between  the  centers  of  gravity  of  the  flanges;  it  cannot  be 
ascertained  definitely  until  the  sizes  of  the  angles  and  the  cover  plates 
are  known.  This  necessitates  a  trial  design,  which  makes  the  method 
somewhat  more  complex  than  that  of  Case  A.  Case  B  is  treated  more 
fully  on  page  223  : 1.  The  method  of  Case  A  is  comparatively  simple 
in  application,  but  it  is  not  well  adapted  to  the  design  of  all  girders  for 
it  would  result  in  a  waste  of  metal  in  some  of  the  heavier  girders.  In 
this  method  the  resisting  moment  of  the  web  plate  is  neglected,  but  this 
is  compensated  for,  in  part,  by  the  use  of  an  increased  depth  (usually 
the  depth  of  the  web  plate).  The  use  of  this  method  gives  safe  results; 
for  girders  without  cover  plates,  or  for  girders  with  6x6  angles  and  a 
single  cover  plate  in  each  flange,  the  results  are  approximately  the  same 
as  those  obtained  by  the  method  of  Case  B  or  C.  Until  the  effect  of 
impact  from  moving  loads  is  better  understood  so  that  different  speci- 
fications are  made  more  nearly  uniform,  and  until  there  is  a  closer  agree- 
ment between  actual  loads  and  those  assumed,  the  method  of  Case  A 
should  give  consistently  good  results  for  the  lighter  girders,  particularly, 
those  mentioned  in  the  preceding  sentence.  Case  A  is  treated  more  fully 
below. 

2.   The  degree  of  accuracy  to  be  used  in  computation  depends  largely 
upon  the  precision  of  the  given  data.    Usually  loads  are  expressed  to  the 


CHAPTER   XXXIII 


THE  DESIGN  OF  PLATE  GIRDERS 


221 


nearest  hundred  pounds,  and  bending  moments  to  the  nearest  hundred 
pound-feet;  bending  moments  which  exceed  1,000,000  pound-feet  may  be 
expressed  to  the  nearest  thousand.  In  Case  A  the  depth  is  taken  to  the 
nearest  tenth  of  a  foot,  whereas  in  Case  B  the  effective  depth  should  be 
taken  to  the  nearest  tenth  of  an  inch.  Net  areas  should  be  expressed  to 
the  nearest  tenth  of  a  square  inch;  this  gives  consistent  accuracy  under 
usual  conditions.  .Many  designers  carry  net  areas  to  hundredths,  but 
this  seems  unnecessary;  the  results  are  usually  identical  whether  tenths 
or  hundreds  are  used,  the  difference  in  thickness  never  exceeding  -fa". 
The  use  of  a  slide  rule  is  recommended  for  all  computations. 

CASE  A 

1.  This  method  is  based  upon  the  following  assumptions: 

(a)  that  the  web  plate  resists  all  the  shearing  stresses; 

(b)  that  the  flange  angles  and  cover  plates  carry  the  whole  flange 
stress  due  to  bending  moment,  the  resisting  moment  of  the 
web  plate  being  neglected; 

(c)  that  the  flange  stress  is  uniformly  distributed  over  the  whole 
flange  area,  the  allowed  average  unit  stress  being  that  speci- 
fied for  the  extreme  fiber;   and 

(d)  that  the  effective  depth  is  taken  equal  to  the  nominal  depth 
of  the  girder,  which  is  usually  the  depth  of  the  web  plate. 

2.  Theory.  —  A  girder  is  designed  so  that  the  resisting  moment  of 
the  horizontal  forces  equals  the  maximum  bending  moment,  as  explained 
on  page  218:2.    In  the  method  of  -Case  A,  the  resisting  moment  of  the 
web  plate  is  neglected;   the  web  plate  is  virtually  a  rectangular  beam  in 
which  the  horizontal   tensile  forces  and   compressive  forces  are  equal 
(page  197:3).    From  page  218:2  it  is  seen  that  the  sum  of  all  tensile  forces 
equals  the  sum  of  all  compressive  forces,  and  it  therefore  follows  that 
the  total  flange  stress  in  the  bottom  (tension)  flange  angles  and  cover 
plates  equals  the  total  flange  stress  in  the  top  (compression)  flange  angles 
and  cover  plates.    Each  of  these  flange  stresses  may  be  represented  by  a 
resultant  force  (F),  as  shown  in  Fig.  221  (a),  and  the  total  resisting  moment 
is  the  product  of  one  force  F  by  the  perpendicular  distance  between  the 
two  forces.     (Two  equal  and  opposite  forces  form  a  couple  and  the  mo- 


ment is  the  same  for  any  point  of  moments.)  In  this  approximate  method 
of  Case  A  the  distance  between  the  resultant  forces  is  taken  for 
convenience  as  the  nominal  depth  of  the  girder  (usually  the  depth  of  the 
web  plate  DW). 

This  is  generally  in  even  inches  and  often  in  even  half  feet.    The  use  of  a  fraction 
of  an  inch  is  not  consistent  with  the  assumptions  upon  which  this  method  is  based; 
if    the   depth    between    the   centers   of 
gravity  of  the  flanges  is  to  be  used  the  .  j"  *> 

girder    should     be    designed     by    the       i 1 I 

method  of  Case  B. 


„, 

In  this  method  the  depth  is  ex- 
pressed to  the  nearest  tenth  of  a 
foot,  so  the  resisting  moment 
FDw  in  pound-feet  is  equated  to 
the  bending  moment  MB  in  pound- 
feet,  thus  :  FDW  =  MB.  The 

flange  stress  is  equal  to  the  unit  stress  multiplied  by  the  net  flange  area, 

MB 


Fig.  221  (a). 


or  F  =  fa.    By  substitution  faDw  =  MB,  whence  a  = 


Thus,  if  we 


divide  the  total  maximum  bending  moment  in  pound-feet  by  the  depth  in 
feet  and  by  the  unit  stress  in  pounds  per  square  inch,  we  obtain  the  re- 
quired net  area  in  square  inches.  The  tension  flange  should  be  designed 
for  this  area  in  the  same  manner  as  a  riveted  tension  member  (pages 
208: 2  and  208:4).  The  maximum  number  of  holes  in  any  one  cross  section 

is  usually  as  indicated  in  Fig.  221  (b)  for  angles 
without  cover  plates,  or  as  in  Fig.  221(c)  when 
cover  plates  are  used;  if  more  than  one  row  of 
rivets  is  used  in  an  angle  leg  the  rivets  are 
staggered.  The  amount  of  stagger  should  not 
be  less  than  that  specified  on  page  305  or  else 
additional  holes  should  be  deducted.  As  a  rule 


Fig.  221  (6).       Fig.  221  (c). 


there  is  little  difficulty  experienced  in  providing  the  proper  stagger  in 
either  leg  of  the  angles  at  the  point  where  the  bending  moment  is  maxi- 
mum, but  it  is  not  usually  feasible  to  attempt  to  make  the  rivets  in  one 
leg  stagger  with  those  in  the  other  leg.  The  design  of  girders  can  best  be 
illustrated  by  typical  problems.  The  solution  of  the  following  problems 


222 


PART  III  — THE   DESIGN   OF  DETAILS 


is  adapted  to  the  tables  found  in  most  handbooks.    The  solution  may  be 
simplified  by  the  use  of  special  tables  in  this  book,  as  explained  below. 

1.  Illustrative  Problem  —  Case  A.  —  Without  Cover  Plates.  —  Design 
an  18-ft.  girder,  composed  of  a  24  x  f  web  plate  and  6  X  4  Ls,  to  sup- 


60-0"c.  to  c.  bearings 


Fig.  222. 

port  a  load  which  causes  a  bending  moment  of  260,000  #ft.    Use  f  "  rivets, 
and  a  unit  stress  of  16,000#/sq.  in. 

80#/ft.  =  31  +  4  x  12  =  approximate  weight  of  girder  (6  X  4  x  f  Ls 

assumed) 

3200#  ft.  =  -^  X  92  =  MB  due  to  weight  (page  188  :  2) 
263,200#  ft.  =  260,000  +  3200  =  total  MB 
263,200 


areas  given  on  page  327;  thus,  after  the  required  net  area  (8.2)  is  found, 
the  following  angles  with  one  f "  rivet  hole  deducted  from  each  angle  may 
be  selected:  6  x  4  x  |,  6  X  3J  x  A,  and  5  X  3|  X  |.  The  relative  weights 
may  be  judged  from  the  same  table.  When  the  usual  unit  stress  of 

16,000#/sq.  in.  is  specified  the  problem 
may  be  still  further  simplified  by  the  use 
of  the  stresses  given  in  the  same  table; 
thus  the  flange  stress  may  be  found  instead 
of  the  net  area  (131,600#  =  263,200-2),  and 
angles  selected  to  give  an  equal  or  greater 
stress  (137,900  for  2Ls6x4xi).  The 
computation  should  be  arranged  preferably 
as  shown  above,  for  reasons  given  on  pages 
185  : 1  and  208  :  3. 

2.  Illustrative  Problem  —  Case  A  —  With 
Cover    Plates.  —  Design    the    60-ft.    girder 

shown  in  Fig.  222  to  carry  a  live  load  of  6000#/ft.  and  a  dead  load  of 
200#/ft.  in  addition  to  its  own  weight.  Use  f  "  rivets,  and  a  unit  stress 
of  16,000#/sq.  in.  Assume  a  depth  of  one-tenth  the  span  with  a  web 
plate  72  x  A  (page  218  :  3). 


"-Center 


8.2   sq.   in. 


=  total  net  area  required  (Dw  =  2  ft.) 


16,000  x  2 
8.6   sq.   in.  =  2(4.75  -  f  x  I)  =  net  area  of  2Ls6  x  4  x  \ 

95#/ft.  =  31  +  4  x  16  =  revised  weight,  using  6  x  4  x  \  angles 

Q^  _  SO 

600#ft.  =  -         -  x  92  =  increase  in  MB 


2 
600 


16,000  x  2 


=  increase  in  net  area,  which  is  negligible. 


107#/ft.  =  weight    of    web    plate     (page    321) 
116#/ft.  =  4  x  29  =  weight  of  6  x  6  x  f  Ls  assumed  (page  303) 
96#/ft.  =  2  x  48  =  weight  of  14  x  1  cover  plates  assumed  (p 

321) 

300#/ft.  =  approximate  total  weight  of  girder  assumed 
200#/ft.  =  other  dead  load 
6000#/ft.  =  live  load 
6500#/ft.  =  total  load 
6500 


By  inspection  we  can  see  that  the  next  lighter  angles  would  be  too 
small.  Therefore  2  Ls  6  X  4  X  §  would  be  used.  If  6  x  4  angles  were 
not  specified,  6  X  3J  or  5  X  3f  angles  might  be  tried  to  see  if  a  reduction 
in  the  amount  of  excess  area  could  be  used  in  order  to  save  metal.  The 
solution  of  this  problem  can  be  simplified  by  the  use  of  the  table  of  net 


2,925,000#  ft.  = 


X  302  =  MB  (page  188  :  2) 


2,925.000 
30.5  sq.  in.  =     '      ' — 5  =  total  net  area  required 

lt),UUU  X  O 

15.9  sq.  in.  =  2(9.73  -  2  x  1  X  1)  =  net    area  2Ls6  X  6  x 
total) 


CHAPTER   XXXIII 


THE   DESIGN  OF  PLATE  GIRDERS 


223 


14.6  sq.  in.  =  30.5  —  15.9  =  net  area  required  in  cover  plates 
\\"  =  1.22"  =  14.6  H-  (14  -  2  x  1)  =  total  thickness  of  cover  plates 
360#/ft.  =  107  +  4  x  33  +  2  x  60  =  revised  weight 
360  -  300 


27,000#  ft.  = 
0.3  sq.  in.  = 


2 
27,000 


X  302  =  increase  in  MB 


=  increase  in  net  area 


Use- 


16,000  X  6 

II"  =1.24"  =  (14.6  +  0.3)  -H  (14  -  2  x  1)  =  revised  thickness  of  cover 
plates  (no  change) 

'  2  Ls  6  x  6  x  | 

L2Pls.l4  x| 

This  design  complies  with  the  specifications  that  the  net  area  of  the 
angles  should  be  as  large  as  that  of  the  cover  plates,  although  the  holes 
in  the  angles  would  have  to  be  either  drilled  or  sub-punched  and  reamed 
(page  30  : 1).  The  net  area  of  the  angles  will  seldom  equal  the  required 
50%,  so  a  slight  excess  will  usually  result;  advantage  may  be  taken  of 
this  excess  by  proportioning  the  cover  plates  for  the  remaining  area 
instead  of  for  the  remaining  50  %.  The  net  area  of  the  plate  is  propor- 
tional to  the  net  width,  as  explained  on  page  208  : 2;  the  required  thickness 
of  plate  is  found  by  dividing  the  net  area  by  the  net  width.  The  com- 
mercial sizes  of  plates  vary  by  sixteenths  of  an  inch  in  thickness;  when 
the  required  plate  thickness  falls  between  two  sizes,  the  thicker  one  should 
be  selected.  If  the  total  thickness  of  plate  exceeds  f  "  it  should  be  sub- 
divided as  explained  on  page  219  : 3;  in  this  problem. two  f"  plates  are 
used.  Note  that  two  rivet  holes  are  deducted  from  each  flange  angle 
when  cover  plates  are  used  (page  221  : 2).  The  solution  of  this  problem 
may  be  simplified  by  the  use  of  the  table  on  page  327  from  which  the 
net  areas  of  angles  may  be  found,  and  the  table  on  page  321  from  which 
the  net  areas  of  plates  may  be  found.  The  net  area  of  a  plate  of  a  given 
width  is  the  same  as  the  gross  area  of  a  plate  whose  width  corresponds 
to  the  net  width  of  the  given  plate;  thus,  the  net  area  of  a  14  x  lj  plate 
is  the  same  as  the  gross  area  of  a  12  x  lj  plate,  the  12  being  the  net 
width  after  two  1"  holes  for  f  "  rivets  are  deducted.  Subsequent  steps 
in  the  complete  design  of  this  girder  are  given  on  pages  248  : 1,  263  : 2, 
264  :  3,  268  :  3,  and  271  :  2. 


CASE  B 

1.  This  method  is  based  upon  the  following  assumptions: 

(a)  that  the  web  plate  resists  all  the  shearing  stresses; 

(b)  that  the  web  plate  also  resists  part  of  the  bending  moment; 

(c)  that  the  flange  stress  is  uniformly  distributed  over  the  whole 
flange  area,  the  allowed  average  unit  stress  being  that  specified 
for  the  extreme  fiber; 

(d)  that  the  resultant  flange  stress  in  each  flange  acts  at  the  center 
of  gravity  of  the  gross  area  of  the  flange  angles  and  cover  plates, 
and  that  the  effective  depth  is  the  distance  between  these 
centers  of  gravity  of  the  two  flanges. 

Note  that  (a)  and  (c)  are  the  same  as  for  Case  A  (page  221  : 1),  but  that 
(6)  and  (d)  differ. 

2.  The  application  of  this  method  involves  two  more  steps  than  the 
method  of  Case  A.     The  effective  depth  depends  upon  the  position  of 
the  center  of  gravity  of  the  flange;   this  cannot  be  determined  until  the 
approximate  sizes  of  the  angles  and  the  cover  plates  are  found  in  a  trial 
design  with  an  assumed  depth.    The  resisting  moment  of  the  web  plate 
is  considered;    the  web  plate  acts  as  a  rectangular  beam,  but  for  con- 
venience an  equivalent  expression  may  be  derived,  so  that  one-eighth 
of  the  gross  area  of  the  web  may  be  treated  as  flange  area  in  conjunction 
with  the  net  area  of  the  angles  and  cover  plates.     Thus,  the  general 
method  of  solution  is  similar  to  that  of  Case  A. 

3.  Theory.  —  The  flange  stress  in  the  angles  and  cover  plates  of  either 
flange  may  be  considered  as  a  single  resultant  force  F  acting  at  the  center 
of  gravity.    The  slight  difference  in  the  position  of  the  centers  of  gravity 
of  the  net  area  and  of  the  gross  area  of  the  angles  and  cover  plates  is 
negligible,  so  the  gross  area  may  be  used  for  convenience.    The  resisting 
moment  of  the  stresses  in  the  flange  angles  and  cover  plates  is  Fdg  (com- 
pare page  221 : 2),  in  which  da  is  the  effective  depth  determined  as  explained 
in  the  following  paragraph.    Since  the  flange  stress  equals  the  unit  stress 
multiplied  by  the  net  area  of  the  angles  and  cover  plates  (if  any),  or 
F  =  fa',  then  the  resisting  moment  Fda  =  fa'dg.    To  this  must  be  added 
the  resisting  moment  of  the  web  plate  acting  as  a  rectangular  beam 


224 


PART   III  — THE   DESIGN   OF  DETAILS 


(page  199:3);  this  resisting  moment  is  \fldwz,  where  t  =  the  thickness 
of  the  web  plate  (i.e.,  the  width  of  the  beam)  and  dw  =  the  depth  of  the 
web  plate.  In  this  method  the  effective  depth,  and  the  thickness  and 
the  depth  of  the  web  are  expressed  in  inches,  so  the  resisting  moment  in 
pound-inches  must  be  equated  to  the  maximum  bending  moment  in 
pound-inches,  thus:  fa'dg  +%ftdw2  =  ms.  Instead  of  using  the  resisting 
moment  of  the  web  plate  in  this  form  it  is  found  to  be  more  convenient 
to  divide  it  by  the  effective  depth  and  by  the  unit  stress  to  give  a  quantity 
which  can  be  combined  with  the  net  flange  area  of  the  angles  and  the 

(1        \  ,VV] 

-^  1  =  a  =  -f-r' 
da  I  Jdg 

In  this  expression  the  full  gross  area  of  the  web  plate  is  used,  no  allowance 
being  made  for  rivet  holes;  but  there  will  be  holes  in  the  web  for  the 
flange  rivets,  and  usually  for  rivets  in  stiffening  angles  (page  266:2). 
There  may  be  no  stiffening  angles  exactly  at  the  point  of  maximum  bend- 
ing moment,  nevertheless  they  may  be  placed  where  the  moment  is  only 
slightly  less.  The  position  of  the  stiffening  angles  and  the  spacing  of 
rivets  cannot  be  determined  until  after  the  girder  is  designed,  so  it  is 
impractical  to  attempt  to  find  the  actual  net  area.  Furthermore,  the 
fraction  of  the  web  plate  counted  as  net  area  is  small  compared  to  the 
net  area  of  the  angles  and  cover  plates,  so  a  slight  variation  will  have 
comparatively  little  effect.  For  convenience,  a  general  method  is  used 
which  provides  for  rivets  under  average  conditions.  Thus  if  we  consider 
-J"  rivets  to  be  spaced  4  inches  center  to  center,  it  means  that  a  1" 
hole  is  deducted  every  4  inches,  leaving  3  inches  of  metal  between ;  thus 
the  net  area  of  the  web  plate  is  f  of  the  gross  area.  The  effect  of 
this  is  to  multiply  the  fraction  £  in  the  expression  given  above  by  f 
making  f.  In  view  of  the  approximation  resulting  from  the  assump- 
tion of  the  size  and  the  spacing  of  the  rivets,  it  is  consistent  and  on  the 

side  of  safety  to  call  -^  equal  to  unity.    Our  revised  formula  then  becomes 
ag 


a'  +  ltda  =  a 


or 


a'  =  a  —  ltdm. 


Thus,  from  the  total  net  area  required  we  subtract  one-eighth  of  the 
gross  area  of  the  web,  leaving  the  net  area  to  be  taken  by  the  angles  and 
cover  plates. 


1.  The  effective  depth  is  expressed  to  the  nearest  tenth  of  an  inch. 
The  distance  from  the  center  of  gravity  of  the  gross  area  of  the  flange 
angles  and  cover  plates  to  the  back  of  the  angles  is  found,*  then  twice 
this  distance  is  subtracted  from  the  depth  of  the  girder  from  back  to 
back  of  angles  to  give  the  effective  depth.  The  depth  from  back  to  back 
of  angles  is  not  the  same  as  the  depth  of  the  web  plate,  but  is  usually 
\"  greater  unless  the  upper  edge  of  the  web  plate  is  unprotected  from 
the  weather  when  it  is  only  \"  greater  (see  page  95  :  3).  Since  the  effective 
depth  cannot  be  determined  accurately  until  the  sizes  of  the  angles  and 
the  cover  plates  are  known,  it  is  necessary  to  make  a  trial  design  with 
an  assumed  depth.  No  convenient  rule  can  be  given  for.  selecting  the 
proper  depth  to  use,  but  an  experienced  designer  is  guided  by  the  results 
of  previous  designs.  In  the  absence  of  more  definite  information  the  fol- 
lowing guides  may  be  used.  For  girders  without  cover  plates  the  problem 
is  comparatively  simple  because  the  distance  from  the  center  of  gravity 
to  the  backs  of  the  angles  does  not  vary  greatly  for  different  thicknesses 
unless  the  size  of  leg  changes.  Thus,  if  the  size  of  the  legs  is  determined 
or  assumed,  the  distance  from  the  center  of  gravity  to  the  back  of  an 
angle  of  intermediate  thickness  may  be  taken  from  the  table  on  page 
325,  and  a  close  approximation  of  the.  effective  depth  may  be  obtained. 
If  angles  of  unequal  legs  with  cover  plates,  or  if  equal-legged  angles  with 
more  than  two  cover  plates  are  used,  the  trial  depth  should  be  taken 
equal  to  the  depth  of  the  web  plate;  but  if  equal-legged  angles  with  only 
one  or  two  cover  plates  are  used,  the  depth  should  be  about  1"  less  than 
the  depth  of  the  -web.  From  the  sizes  of  the  angles  and  cover  plates 
found  as  a  result  of  the  trial  design  the  corrected  effective  depth  should 
be  found  to  the  nearest  tenth  of  an  inch.  The  bending  moment  due  to 
the  weight  of  the  girder  should  be  revised  also,  and  a  second  solution 
of  the  problem  should  be  made.  If  the  sizes  of  the  angles  or  cover  plates 
differ  from  those  found  in  the  trial  design  the  corresponding  effective 

*  For  convenience  the  point  of  moments  is  taken  at  the  back  of  the  angles.  Th« 
difference  between  the  product  of  the  gross  area  of  the  angles  by  the  distance  to  th< 
center  of  gravity  of  the  angles  and  the  product  of  the  gross  area  of  the  cover  platei 
by  one-half  the  total  thickness  of  cover  plates,  is  divided  by  the  sum  of  these  gross 
areas;  the  resultant  distance  is  measured  toward  the  angles  or  toward  the  cove) 
plates  according  to  which  of  the  above  products  is  larger. 


CHAPTER   XXXIII 


THE   DESIGN  OF  PLATE  GIRDERS 


225 


depth  should  be  determined;  a  third  design  is  not  necessary  provided 
the  corrected  effective  depth  does  not  differ  from  the  depth  used  in  the 
second  design  by  more  than  0.1"  for  girders  less  than  3  ft.  deep  nor  by 
more  than  j"  for  deeper  girders. 

1.  Illustrative  Problem  —  Case  B. —  Design  the  girder  shown  in 
Fig.  225,  for  a  60-foot  single-track  through  railway  bridge  to  support 
Cooper's  E60  live  load,  using  the  specifications  of  the  American  Rail- 
way Engineering  Association.  We  will  use  J"  rivets,  and  assume  a  72 x^ 
web  plate  (see  page  218  :  3).  The  length  is  divided  into  four  equal  panels 
of  15  ft.,  and  the  width  of  the  bridge  from  center  to  center  of  girders  is 

14'  6".    The  total  dead  load  of  the  track  

is  taken  as  450#/ft.,  including  the  rails, 
the  ties,  the  guard  rails,  the  splice  bars, 
the  fastenings,  etc.  The  design  of  the 
stringer  and  floor  beam  naturally  pre- 
cedes the  design  of  the  girder ;  we  will 
assume  that  these  have  been  designed 
and  that  the  weights  have  been  deter- 
mined to  be  150#/ft.,  for  each  stringer 
and  175#/ft.  for  each  floor  beam.  The 

maximum  concentrated  live  loads  trans-  ]< « 

mitted  from  the  floor  beams  to  this  girder  ^ 

were  found  on  page  196  : 2  to  be  39,900#, 
82,000#,  and  52,100,  respectively;  to  these 

should  be  added  the  corresponding  impact  allowance  for  the  effects  of 
moving  loads,  and  also  the  dead  loads,  to  give  the  total  concentrated  loads. 
The  bending  moment  due  to  these  concentrated  loads  should  be  increased 
by  the  bending  moment  due  to  the  assumed  weight  of  the  girder  itself  which 
is  uniformly  distributed.  The  allowance  for  impact  stresses  is  provided 
for  in  the  specifications  in  the  form  of  a  percentage  of  the  live  load.  In 
the  A.R.E.A.  specifications  mentioned  above  this  percentage  is  deter- 

300 
mined  from  the  expression  *  T    |         ,  in  which  L  is  the  length  of  track  in 


feet  which  must  be  loaded  to  cause  the  maximum  live-load  strain  in  the 
member.  In  this  problem  the  maximum  bending  moment  in  the  girder 
will  be  found  when  the  track  is  loaded  for  the  entire  length  of  the  girder, 

300 
hence  the  impact  percentage  is  ^:.    The  solution  follows: 

3Vr   .  _r..14.5 


=  dead  load  at  each  panel,  due 


80 


6900#  =  (^~  +  150)  15  +  175  X 

to  track,  stringers,  and  floor  beam 
,100#  =  39,900  f  1  +ij||j)  +  6900  =  total  load  at  1st  panel  point 


154" 


^Center 


6Q'-0"C:  to  c.  bearings 


1 


Fig.  225. 


_  /       300\  _ 

V       360/ 


*  A  change  to 


30,000 


30,000  +  If 

tion  and  it  has  not  yet  been  adopted. 


L  +  300' 
has  been  recommended  but  it  is  meeting  with  opposi- 


102,400# 
164,300# 

3,728,000#ft. 
370#/ft. 


o; 

,300\ 

\-^^    +  olJUU 


„       „ 


it       u      it 


3rd 


52,100 

(80,100  x  3  +  157,200  x  2  +  102,400  x  1)  -s-  4  =  left-hand 

reaction 
164,300  X  30  -  80,100  x  15  =  MB  due  to  cone,  loads  (Fig. 

251  (a)). 
107+4x29+2x71=approx.   weight   of  girder   (6x6xf  Ls 

and  14  x  If  cover  plates  assumed) 
370 


167,000#ft.  =  -^  X  302  =  MB  due  to  weight  of  girder 


226 

3,895,000#ft. 

40.6  sq.  in. 

3.9  sq.  in. 

36.7  sq.  in. 
13.9  sq.  in. 


PART  III  — THE   DESIGN   OF  DETAILS 


3,728,000  +  167,000  =  total  MB 

=  total  net  area  required  (d,  assumed  72") 


22.8sq.  in.  = 
1ft"  =  1.90"  = 

0.09"  = 


72.3" 
410#/ft. 


x 

5  X  72  x  i7  =  I  the  gross  area  of  the  web 
net  area  required  in  angles  and  cover  plates 
2(8.44  -  2  x  1  X  f)  =  net  area  2Ls6  x  6  X  5   (see  page 

303) 

balance  required  in  cover  plates    ' 
22.8  -=-  (14  -  2  x  1)  =  thickness  of  14"  cover  plates 

2  x8.44  x  1.78  -27.13  x  0.97 

tfi  OQ   ,  OT  IQ  '  =  distance  from  back  of 

10. oo  +  &l .  Lo 

angles  to  center  of  gravity  (Fig.  226) 
72 +  0.5-2x0. 09  =  effective  depth  da 
107  +4x29  +  2x92  =  revised  weight  of  girder 
410 


185,000#ft.  =  -y  X  302  =  revised  MB  due  to  weight  of  girder 

3,913,000#ft.  =  3,728,000  +  185,000  =  revised  total  M  B 

3,913,000  x  12 
40.6  sq.  in.  =    '       '        T0  „  =  revised  total  net  area 

lOjUUU  X  /^£.o 

r2Ls6  x6  xf 
Use  |  1  P1.14  x  U 

12P1S.14X|  A.ofP',.=27J3 

Fig.  226. 

Note  that  the  revised  total  area  is  the  same  as  the  first  total,  so  no 
further  revision  is  necessary;  this  is  because  the  increase  due  to  increased 
weight  happened  to  compensate  the  decrease  due  to  the  larger  depth. 
Had  there  been  a  difference  in  area,  the  balance  (22.8)  required  in  the 
cover  plates  could  have  been  changed  by  a  like  amount  and  the  cor- 
responding thickness  could  have  been  found.  For  comments  upon  the 
arrangement  see  pages  185  : 1  and  208  :  3.  For  suggestions  upon  the  solu- 
tion see  page  222 : 2.  Subsequent  steps  in  the  complete  design  of  this 
girder  are  given  on  pages,  226  : 1,  250:3,  262  : 1,  265  : 1,  269  : 1,  and  273  : 1. 
1.  Railway  bridges  and  viaducts  are  subject  to  lateral  forces  due  to 
the  effects  of  the  rocking  or  "  nosing  "  of  the  locomotives,  and  of  the 


wind  pressure  both  upon  the  structures  themselves  and  upon  passing 
trains.    These  lateral  forces  are  often  treated  together.     They  act  hori- 
zontally and  they  are  resisted  by  the  bracing  systems.     The  effects  of 
the  train  are  most  severe  upon  the  "  loaded  chords,"  i.e.,  the  top  flange 
of  stringers  and  deck  girders,  or  the  bottom  flanges  of  through  girders. 
The  American  Railway  Engineering  Association  specifies  a  lateral  force 
of  200#/  ft.  on  the  unloaded  chord,  while  on  the  loaded  chord  this  is 
increased  by  10  %  of  the  specified  train  load  which  follows  the  engines ; 
both  are  considered  as  moving  loads.    The  bending  moment  due  to  these 
lateral  forces  cannot  be  combined  with  the  bending  moment  due  to  the 
vertical  forces  because  they  act  in  different  planes;   but  the  correspond- 
ing flange  stresses  or  flange  areas  can  be  added.     The  lateral  bracing- 
forms  the  web  system  of  a  horizontal  truss,  the  chords  of  which  are  the 
flanges  of  the  girders.     By  the  method  of  sections  the  stress  in  one  o ' 
the  chords  at  the  center  is  found  by  dividing  the  sum  of  the  moment:; 
of  the  external  forces  on  one  segment  by  the  depth  of  the  truss,  i.e.,  the 
perpendicular  distance  between  girders.     The  sum  of  the  moments  i; 
equivalent  to  the  bending  moment  of  the  uniformly  distributed  latera 
forces,  even  though  the  forces  are  concentrated  at  the  floorbeams.    Sine' 
the  maximum  flange  stress  due  to  the  vertical  forces,  and  the  maximun 
flange  stress  due  to  the  horizontal  forces  are  not  likely  to  occur  simul 
taneously,  it  is  customary  to  neglect  the  latter  unless  the  combined  stres 
per  square  inch  exceeds  by  more  than  25  %  the  unit  stress  allowed  fo 
vertical  forces  alone.    When  the  combined  stress  does  exceed  this  amoun 
the  flange  should  be  strengthened.     The  effect  of  lateral  forces  upo 
the  problem  of  page  225  : 1  should  be  considered  as  follows : 

800#/ft.  =  200  +  6000  x  0.10  =  specified  lateral  force  on  bottom  chor 
800 


360,000#  ft. 


1.6  sq.  in.  = 


X  302  =  MB  due  to  lateral  force 


360,000 


16,000  x  14.5 


=  corresponding  net  area  required. 


This  is  less  than  25  %  of  the  net  area  40 . 6  which  is  required  by  t\ 
vertical  forces  alone;  hence  the  combined  unit  stress  will  not  excee 
16,000  x  1 . 25,  and  no  change  in  section  need  be  made. 


CHAPTER   XXXIII 


THE   DESIGN  OF  PLATE  GIRDERS 


227 


1.  The  method  of  designing  heavy  girders  with  vertical  flange  plates, 
with  four  angles  in  each  flange,  or  with  both,  is  similar  to  the  method 
of  Case  B   (page  223  : 3)  only  somewhat  more  complex.     The  effective 
depth  is  the  distance  between  the  centers  of  gravity  of  the  gross  area 
of  the  flange  angles,  the  cover  plates,  and  the  vertical  flange  plates.    One- 
eighth  of  the  gross  area  of  the  web  plate  may  be  counted  as  flange  area. 
It  is  assumed  that  only  experienced  designers  will  have  occasion  to  design 
girders  of  this  type,  so  that  further  comments  would  be  out  of  place  here. 

2.  Girders  which  support  curved  railroad  tracks  should  be  designed 
to  resist  centrifugal  forces.    These  forces  vary  with  the  degree  of  curva- 
ture and  with  the  weight  and  the  velocity  of   the  train.    The  forces  are 
treated  as  uniformly  distributed   horizontal  forces  for  which  the  hori- 
zontal bending  moment  and  the  corresponding  flange  stress  or  flange  area 
must  be  found  in  the  same  manner  as  for  lateral  forces  (see  above).    The 
flange  should  be  designed  for  the  sum  of  this  area  and  the  area  found 
from  the  vertical  forces,  no  increase  in  unit  stress  being  allowed  as  for 

lateral   forces.     The  amount  of  centrifugal  force  is  ^    ^  in  pounds  per 


linear  foot  applied  at  the  top  of  the  rails,  where  U  =  the  equivalent  uni- 
formly distributed  live  load  which  will  produce  the  same  live-load  bend- 
ing moment  used  in  the  design,  V  =  the  velocity  of  the  train  in  feet  per 
second,  and  R  =  the  radius  of  the  curve  in  feet.  The  velocity  is  often 
specified  as  60  -  2|Z)  miles  per  hour,  where  D  =  the  "  degree  "  of  curva- 
ture in  degrees.  By  substituting  an  equivalent  expression  in  feet 
per  second  for  V,  and  the  approximate  value  of  5730  -f-  D  for  R 
we  obtain  the  following  more  convenient  expression  for  centrifugal 


force  = 


£7.0(24  -  Z))2  . 


in  pounds  per  linear  foot.     If  the  length  of  the 


13,700 

span  is  long,  or  the  degree  large,  it  may  become  necessary  to  take  into 
account  the  eccentricity  of  the  load  on  the  bridge  whereby  one  girder 
receives  more  than  one-half  the  load.  This  is  treated  more  fully  in  books 
on  Bridge  Design.* 

*  For  example,  Kirkham's  "Structural  Engineering,"  McGraw-Hill  Book  Co.,  Inc., 
New  York;  Waddell's  "Bridge  Engineering,  "  John  Wiley  and  Sons,  Inc.  New  York;  or 
Marburg's  "Framed  Structures  and  Girders,"  Part  I,  McGraw-Hill  Book  Co.,  Inc., 
New  York. 


CHAPTER  XXXIV 
THE  THEORY  AND  PRACTICE  OF  RIVETING 

SYNOPSIS:  A  general  discussion  of  the  construction  of  riveted  joints  and  of  how 
their  strength  is  determined.  The  application  of  the  principles  involved  to  typical 
problems  is  shown  in  subsequent  chapters. 


1.  Rivets  are  used  to  connect  the  different  members  of  a  structure 
to  one  another  and  also  to  fasten  together  the  component  parts  of  each 
member.    A  rivet  is  composed  of  a  cylindrical  shank  with  a  head  at  one 
end.    The  holes  in  the  parts  to  be  connected  are  made  ^"  larger  than 
the  nominal  diameter  of  the  rivet  shank  so  that  the  rivet  may  be  inserted 
more  easily.     The  length  of  the  rivet  must  be  greater  than  the  thickness 
of  the  metal  through  which  it  passes,  so  that  enough  metal  will  protrude 
to  form  the  second  head.    The  rivet  is  heated,  then  put  in  position  and 
"  driven  "  until  the  second  head  is  formed  and  the  shank  is  upset  to 
fill  the  enlarged  hole,  as  explained  on  page  30  : 4.     The  parts  connected 
are  held  in  position  by  temporary  bolts  until  rivets  are  driven  in  the 
remaining  holes,  after  which  the  bolts  are  replaced  by  rivets.     For  this 
reason  no  piece  should  be  connected  by  less  than  two  rivets.    Conditions 
sometimes  justify  the  use  of  a  single  bolt  but  never  a  single  rivet  lest  the 
piece  become  twisted  during  the  process  of  riveting. 

2.  Shop  and  Field  Rivets.  —  Rivets  which  are  driven  in  the  shop  are 
more  effective  than  those  driven  in  the  field.     Shop  rivets  are  usually 
driven  by  machines  which  develop  sufficient  pressure  to  insure  complete 
upsetting.    Field  rivets  must  be  driven  by  smaller  machines  or  by  hand. 
In  the  shop,  the  members  are  conveniently  supported  by  skids,  trucks, 
or  cranes.    In  the  field,  the  rivets  must  be  driven  at  a  disadvantage  on 
account  of  their  comparatively  inaccessible  positions  in  the  structure. 
It  is  customary  to  allow  a  smaller  unit  stress  for  field  rivets,  than  for 
shop  rivets.     It  is  therefore  imperative  that  the  draftsman  know  which 


rivets  are  driven  in  the  shop  and  which  in  the  field.  In  general,  shop 
rivets  are  used  wherever  possible  because  they  are  not  only  better,  but 
they  can  be  driven  more  cheaply.  Field  rivets  must  necessarily  be  used  for 
connecting  to  each  other  members  which  are  shipped  separately,  but  shop 
rivets  are  used  for  holding  the  component  parts  of  each  member  together. 

3.  Position  in  Member.  —  Rivets  are  driven  at  right  angles  to  the 
line  of  the  stress  which  they  are  to  transmit  from  one  part  to  another. 
The  number  of  rivets  required  in  an   ordinary  connection  is  found  by 
dividing  the  total  stress  by  the  limiting  value  of  one  rivet.    This  limiting 
value  will  now  be  considered. 

4.  The  design  of  a  riveted  joint  is  based  upon  several  assumptions. 
Some  of  these  are  disputable,  but  the  error  in  one  assumption  often  tends 
to  compensate  the  .error  in  another,  so  that  the  results  obtained  are  quite 
satisfactory.     The  usual  assumptions  are  that: 

the  driven  rivet  completely  fills  the  hole, 

the  effective  area  of  a  compression  member  is  not  reduced  by  the 

rivets, 

the  stress  in  a  tension  member  is  distributed  uniformly  over  the 

net  area  of  cross  section, 

the  stress  is  equally  distributed  among  all  the  rivets  of  .an  ordinary 

concentric  joint, 

(e)   the  friction  between  adjacent  parts  is  neglected, 
(/)  the  bending  of  the  rivets  is  ignored  except  for  long  rivets,  and 
(g)  rivet  heads  should  not  be  subjected  to  tension. 


(a) 


(c) 
(d) 


228 


CHAPTER   XXXIV 


THE  THEORY  AND  PRACTICE  OF  RIVETING 


229 


Assumptions  (a),  (6),  and  (c)  are  made  in  the  design  of  tension  and 
compression  members  (pages  206:4  and  211  :  2).  Shop-driven  rivets 
probably  fill  the  holes  because  sufficient  pressure  is  exerted  to  compress 
the  rivets  enough  to  overcome  any  shrinkage  due  to  the  rivets  cooling. 
Field  rivets  do  not  so  surely  fill  the  holes  but  this  fact  is  discounted  in 
the  specifications  by  allowing  a  lower  unit  stress.  Inspectors  should 
test  each  rivet'  with  a  hammer,  and  loose  rivets  should  be  redriven.  A 
slight  looseness  probably  would  not  impair  the  strength  of  a  connection 
materially  after  the  "  initial  slip  "  has  taken  place,  unless  subjected  to 
alternate  tensile  and  compressive  stresses.  That  the  stress  is  equally 
distributed  among  all  the  rivets  (assumption  d)  is  impossible  as  may  be 
seen  from  Fig.  229  (a).  This  shows  two  bars  fastened  together  by  three 
rivets.  The  total  stress  is  18,000#.  If  the  first  rivet  transmits  a  third 

of  the  total  stress  from  one  bar  to 

60(0^2000  r^,mnn  the  other,  then  between  the  first  two 

aooo  6000  rivets  one  bar  would  carry  6000  and 

Fig.  229  (a).  the  other  12,000.  Since  the  strain 

is  proportional  to  the  stress  (page 
197:3)  the  distance  .  between  rivets  could  not  be  kept  equal  in  the 
two  plates  unless  the  area  of  each  bar  was  changed  at  each  rivet 
which  would  be  impractical.  This  difference  in  distance  would  at  once 
cause  unequal  distribution  of  the  stress  among  the  rivets.  It  is  prob- 
able, however,  that  the  average  value  of  the  rivets  in  a  concentric 
connection  is  constant,  and  the  allowed  unit  stress  may  be  considered 
an  average  value.  Eccentric  connections  must  be  treated  differently, 
as  explained  in  Chapter  XXXVI,  page  237.  The  friction  between 
the  adjacent  parts  of  a  riveted  joint  (assumption  e)  is  considerable, 
especially  when  the  rivets  act  in  double  shear  and  are  machine 
driven.  The  American  Bridge  Company  has  found  from  the  tests  on 
their  standard  beam  connections  (page  83  : 6)  that  when  the  web  is 
enclosed  between  two  connection  angles,  the  value  of  each  rivet  is  about 
25%  greater  than  when  a  single  angle  is  used.  This  is  on  account  of 
the  friction.  Except  for  these  angles  used  under  average  conditions, 
it  is  common  practice  at  present  to  ignore  friction.  The  consequent 
increased  efficiency  compensates  at  least  in  part  for  the  deficiencies  due 
to  the  other  assumptions.  Although  the  effect  of  bending  short  rivets 


is  disregarded  (assumption  /),  the  bending  of  long  rivets  must  be  con- 
sidered. It  is  unnecessary  to  design  them  as  cylindrical  beams  as  in 
the  case  of  pins  (Chapter  XLI,  page  278).  More  commonly  the  number 
of  rivets  is  increased  when  the  grip  of  the  rivets  (i.e.,  the  thickness  of 
the  parts  connected)  is  more  than  four  times  the  diameter.  The  usual 
increase  in  number  is  1  %  for  each  additional  sixteenth  of  an  inch  in  the 
grip.  See  page  235  : 2  for  the  effect  of  loose  fillers.  The  effect  of  axial 
tension  on  rivets  (assumption  g)  is  not  well  understood.  Many  engineers 
maintain  that  no  dependence  should  be  placed  upon  rivets  in  tension 
because  the  heads  are  liable  to  be  pulled  off.  Others  maintain  that  con- 
siderable tension  can  be  resisted,  and  tests  substantiate  their  claim,  but 
the  safe  values  to  allow  have  not  been  definitely  determined.  It  is  better 
wherever  possible  to  avoid  connections  in  which  rivets  are  subjected  to 
axial  tension.  If  this  is  impractical  it  is  well  to  substitute  bolts  for  the 
rivets,  because  they  are  stronger  in  direct  tension. 

1.  A  riveted  joint  is  designed  to  resist  the  tendency  to  shear  the  rivets, 
and  the  tendency  for  the  rivets  to  tear  through  one  or  more  of  the  con- 
nected parts.  The  action  of  the  shearing  forces  may  be  visualized  by 
imagining  a  small  hole  bored  through  two  overlapping  steel  plates  and 
an  ordinary  wooden  match  stick  driven  through  the  hole.  If  one  plate 
is  made  to  slide  along  the  other,  the  wooden  match  will  be  sheared  off 
as  if  cut  by  shears.  Similarly,  if  three  pieces  of  cardboard  are  placed 
together  with  a  wooden  match  passing  through  them,  and  the  middle 
piece  is  slipped  along  the  other  two,  remaining  in  contact,  the  match 
will  tear  through  the  cardboard.  A  riveted  joint  may  fail,  therefore, 
either  in  shear,  by  the  shearing  of  the  shanks  of  the  rivets,  or  in  bearing, 
by  the  rivets  tearing  through  one  or  more  of  the  connected  parts.  A 
tension  joint  may  also  fail  in  one  of  three  other  ways, 
1st,  in  tension,  by  one  of  the  parts  tearing  along  the 
line  of  least  resistance;  this  must  be  considered  in  the 
design  of  the  main  member  (Chapter  XXXII,  page 
206),  and  in  the  design  of  the  details,  as  for  example 
page  286  : 1.  2nd,  by  the  rivets  tearing  out  at  the 
edges  of  one  or  more  parts;  this  may  be  prevented  by 
the  use  of  standard  edge  distances  (page  69  : 3)  which  are  determined 
accordingly  (compare  page  256  : 3).  3rd,  by  the  bending  of  a  lap  joint 


Fig.  229  (6). 


230 


PART   III  — THE   DESIGN   OF  DETAILS 


so  that  the  rivet  heads  are  pulled  off,  as  shown  exaggerated  in  Fig.  229  (6) ; 
this  is  unusual  and  is  not  an  important  consideration  except  in  tank  and 
pipe  work.  The  limiting  value  of  one  rivet  in  a  joint  designed  for  tension 
or  for  compression  is  determined  either  by  the  resistance  in  shear  or  in 
bearing,  whichever  is  less. 

1.  The  strength  of  one  rivet  in  either  shear  or  bearing  is  determined 
from  the  nominal  diameter  and  not  from  the  diameter  of  the  driven  rivet 
after  it  has  been  upset  to  fill  the  hole  which  is  usually  iV  larger.    Most 
specifications  have  clauses  to  this  effect.    On  account  of  the  inaccuracies 
of  the  shop  work,  the  holes  in  different  connecting  parts  may  not  be  in 
perfect  alignment,  and  hence  the  upset  shank  will  not  be  a  true  cylinder. 
As  a  result,  the  effective  area  of  cross  section  of  the  rivet  in  the  plane  of 
contact  of  the  connected  parts  may  not  exceed  the  nominal  area.    Since 
the  rivet  tends  to  shear  along  this  plane  it  is  important  that  the  shearing 
value  be  limited  to  the  strength  of  the  rivet  before  upsetting.     For  the 
sake  of  uniformity  and  to  provide  for  the  incomplete  upsetting  of  the 
rivet  it  is  customary  to  limit  the  bearing  value  in  a  similar  manner. 

2.  The  strength  of  a  rivet  in  shear  depends  upon  the  area  of  cross 
section  of  its  shank,  which  is  the  area  of  a  circle  of  a  diameter  equal  to 

the  nominal  diameter  of  the  rivet.  The  different 
parts  connected  may  be  so  arranged  that  the  rivets 
will  tend  to  shear  in  either  one  or  two  planes.  If 
all  the  parts  which  tend  to  move  in  one  direction  are 


Fig.  230  (a). 


on  the  same  side  of  the  parts  which  act  in  the  opposite  direction,  the  rivets 
tend  to  shear  in  one  plane,  as  shown  in  Fig.  230  (a),  and  they  are  said  to 
be  in  "  single  shear."  If  the  parts  which  act  in  one  direction  are  between 
the  parts  which  act  in  the  opposite  direction,  the  rivets  tend  to  shear  in 
two  planes,  as  shown  in  Fig.  230  (6),  and  they  are 
said  to  be  in  "  double  shear."  In  ordinary  practice 
it  is  unnecessary  to  consider  more  than  two  shearing 
planes.  The  first  step  in  finding  the  limiting  value 


Fig.  230(6). 


of  one  rivet  is  to  determine  whether  the  rivets  are  in  single  or  double  shear. 
The  unit  stresses  in  shear  on  shop  rivets  allowed  by  different  specifications 
are  10,000,  11,000,  or  12,000  pounds  per  square  inch.  The  correspond- 
ing values  for  field  rivets  are  8000,  9000,  and  10,000.  The  strength  of 
i,  rivet  in  single  shear  is  equal  to  the  area  of  a  circle  of  a  diameter  equal 


to  the  nominal  diameter  of  the  rivet  multiplied  by  the  allowed  unit  stress 
per  square  inch.  The  strength  of  a  rivet  in  double  shear  is  twice  that 
of  the  same  rivet  in  single  shear  because  the  resisting  area  is  doubled. 
Rivet  values  are  tabulated  at  the  end  of  the  book,  as  explained  on  page 
231  : 1. 

3.  The  strength  of  a  rivet  in  bearing  depends  upon  the  diameter  of 
the  rivet  and  the  thickness  of  the  metal  in  which  it  bears.    The  bearing 
surface  is  cylindrical,  but  it  can  offer  no  more  resistance  to  forces  parallel 
to  the  line  of  stress  than  a  flat  surface,  if  indeed  as  much,  as  shown  in 
Fig.  230  (c).    The  effective  area  is  therefore  considered  to  be  a  rectangle, 
the  dimensions  of  which  are  the  nominal  diameter  of  the  rivet  and  the 
thickness  of  the  metal  in  which  it  bears.    If  two  plates  of  different  thick- 
nesses are  riveted  together,  the  rivets  would  naturally  tear  through  the 
thinner  plate  before  they  would  through  the  thicker  plate,  and  the  bear- 
ing value  of  each  rivet  would  be  determined  by  the  thick- 
ness of  the  thinner  plate.    If  more  than  two  parts  are     )       —$-*.      1 
connected  by  the  same  rivets,  the  rivets  would  have  to     I      ^jgz)     j 

tear  through  all  the  parts  which  act  in  the  same  direction    I \ 

and  not  merely  through  a  single  part.     The  bearing  value       pig.  230  (c). 
of  each  rivet  would  then  be  determined  by  the  thinner 

combined  thickness  of  all  the  parts  which  act  in  either  direction,  and  not 
necessarily  by  the  thickness  of  the  thinnest  part.  This  is  true  whether  the 
rivets  are  in  single  or  double  shear.  Thus  in  Figs.  230  (a)  and  (6),  the 
total  thickness  of  the  two  plates  acting  toward  the  left  should  be  com- 
pared with  the  total  thickness  of  the  two  plates  acting  toward  the  right, 
and  the  smaller  value  used  in  determining  the  bearing  value  regardless 
of  whether  the  plates  which  act  in  one  direction  are  together  as  in  (a),  or 
separated  as  in  (6).  The  unit  stress  in  bearing  allowed  by  the  specifica- 
tions is  usually  twice  the  corresponding  unit  stress  in  shear.  The  strength 
of  a  rivet  in  bearing  is  equal  to  the  unit  stress  multiplied  by  the  product 
of  the  nominal  diameter  of  the  rivet  by  the  limiting  thickness  of  metal 
explained  above.  Rivet  values  are  tabulated  at  the  end  of  the  book,  as 
explained  on  page  231  : 1. 

4.  Bolts  (except  specially  fitted  turned  bolts)  do  not  fill  the  holes  and 
they  are  not  so  effective  in  shearing  or  in  bearing  as  rivets.     They  are 
not  used  in  important  connections,  but  they  are  often  used  for  holding 


CHAPTER   XXXIV 


THE  THEORY  AND  PRACTICE  OF  RIVETING 


231 


secondary  members  in  position.  The  unit  stress  in  shear  is  usually  taken 
about  1000  pounds  per  square  inch  less  than  the  unit  stress  for  field 
rivets.  It  is  sometimes  specified  as  two-thirds  the  value  for  field  rivets. 
The  unit  stress  in  bearing  is  twice  the  unit  stress  in  shear. 

1.  To  find  the  number  of  rivets  required  in  an  ordinary  connection, 
first  decide  whether  they  are  to  be  shop  or  field  driven,  and  whether  they 
are  in  single  or  double  shear.  Find  the  corresponding  shearing  value 
of  one  rivet  of  the  given  diameter  for  the  specified  unit  stress.  Next 
determine  the  limiting  thickness  of  metal  and  find  the  corresponding 
bearing  value.  The  smaller  of  these  two  values  is  the  limiting  value  of 
one  rivet,  and  the  number  of  rivets  required  may  be  found  by  dividing 
the  total  stress  by  this  limiting  value.  By  means  of  the  tables  mentioned 
below,  the  number  of  rivets  may  be  found  directly  opposite  the  value 
which  equals  or  exceeds  the  given  total  stress.  The  limiting  value  may 
not  be  the  same  for  all  of  the  rivets  in  a  given  connection  because  some 
may  be  in  single  shear  and  the  rest  in  double  shear,  or  else  some  rivets 
may  have  a  different  bearing  value  from  the  rest.  In  this  event  the 
strength  of  the  rivets  with  one  limiting  value  must  be  added  to  that  of 
the  rivets  with  another  limiting  value  to  give  the  total  strength  of  the 
connection.  Tables  of  rivet  values  are  given  on  pages  308  to  311, 
one  page  for  each  diameter  of  rivet.  On  each  page  are  values  for  unit 
shearing  stresses  varying  by  thousands  from  7000  to  12,000  pounds 
per  square  inch,  and  bearing  values  for  unit  stresses  which  are  twice  as 
great.  Other  values  may  be  found  by  direct  proportion.  The  values 
for  unit  stresses  commonly  specified  for  shop  rivets  are  given  at  the  left 
of  each  page,  and  opposite  these  are  values  for  field  rivets  and  bolts  which 
are  usually  allowed  by  the  same  specifications.  The  values  in  the  upper 
table  are  specified  by  the  American  Railway  Engineering  Association^ 
and  are  hi  common  use.  In  each  group  are  given  the  single  and  double 
shear  values  and  the  bearing  values  in  different  thicknesses  of  metal  not 
only  for  one  rivet  but  for  any  number  from  one  to  ten.  Values  for  more 
than  ten  rivets  may  be  found  by  addition  or  by  multiplication,  as  for 
example,  the  value  for  14  rivets  is  the  sum  of  the  values  for  10  and  4 
rivets,  is  twice  the  value  of  7  rivets,  or  is  14  times  the  value  for  1  rivet. 
If  desired,  the  value  for  one  rivet  may  be  found  to  one  more  decimal  place 
by  dividing  the  value  for  10  rivets  by  10.  For  convenience  a  dotted 


line  is  placed  in  the  table  of  bearing  values  to  show  the  relation  of  the 
shearing  value.  All  bearing  values  to  the  left  of  the  dotted  lines  are  less 
than  the  single  shear  value,  while  all  to  the  right  are  greater  than  for 
single  shear  and  less  than  for  double  shear.  The  bearing  values  in  metal 
thicker  than  the  thicknesses  shown  are  greater  than  for  double  shear. 
In  the  tables  the  bearing  values  are  given  only  for  thicknesses  which 
are  multiples  of  ^".  It  is  usually  close  enough  to  take  the  web  thicknesses 
of  I-beams  and  channels  to  the  nearest  sixteenth  from  the  tables  on 
pages  322  or  323,  although  more  exact  values  may  be  found  by  multi- 
plying the  web  thicknesses  in  hundredths  by  the  rivet  diameter  and  by 
the  unit  stress.  Except  for  large  numbers  of  rivets,  the  latter  method 
should  not  be  necessary.  The  fractions  given  in  the  tables  mentioned 
above  should  be  used  in  preference  to  those  given  on  pages  298  to  301 
because  in  some  cases  they  are  -jV'  less,  as  explained  at  the  tops  of  the 
tables.  The  former  are  used  in  designing,  for  the  sake  of  safety,  while 
the  latter  are  used  in  drafting,  for  the  sake  of  clearance. 

2.  Flattened  and  Countersunk  Rivets.  —  It  is  often  necessary  to 
flatten  rivet  heads  to  f "  or  \"  in  height  in  order  to  furnish  clearance  for 
erecting  other  members.  A  flattened  rivet  may  be  considered  as  strong 
as  an  ordinary  button-head  rivet.  The  effective  part  of  the  rivet,  i.e., 
the  upset  shank,  is  the  same  for  both  since  only  the  head  is  altered  in 
shape.  Countersunk  rivets  are  used  instead  of  flattened  rivets  when 
greater  clearance  is  required.  A  countersunk  rivet  head  is  shaped  as 
shown  on  page  304,  and  the  rivet  hole  must  be  reamed  out  or  recessed 
to  provide  space  for  the  head,  much  as  hard  wood  is  reamed  to  provide 
for  the  head  of  an  ordinary  flat-headed  wood  screw.  The  head  of  a 
countersunk  rivet  may  hot  fit  the  reamed  hole  exactly,  hence  it  may 
not  be  flush  with  the  surface  of  the  piece  in  which  it  is  countersunk.  If 
necessary,  any  projection  should  be  chipped  off  with  a  pneumatic  chisel, 
or  otherwise,  to  provide  a  smooth  bearing  surface.  This  is  done  on  the 
bottoms  of  bearing  plates  so  that  the  whole  plates  will  rest  on  the  sup- 
ports and  not  simply  on  the  rivet  heads.  The  heads  are  also  chipped 
if  another  steel  surface  is  to  be  placed  in  contact  after  the  rivets  are 
driven.  Countersunk  rivets  may  be  used  without  being  chipped  where 
a  slight  projection  is  not  objectionable,  but  where  a  rivet  flattened  to 
\"  would  project  too  much.  A  countersunk  rivet  will  not  project  over  j". 


232 


PART   III  — THE   DESIGN   OF  DETAILS 


Practice  is  not  uniform  regarding  the  strength  of  countersunk  rivets. 
Some  engineers  use  them  for  holding  fillers  and  base  plates  in  position, 
but  never  count  upon  their  carrying  much,  if  any,  direct  stress.  Other 
engineers  count  them  one-half  as  strong  as  button-head  rivets.  If  the 
thickness  of  metal  in  which  a  rivet  is  countersunk  is  no  greater  than 
the  depth  of  the  head  (page  304),  the  entire  bearing  of  the  plate  on 
the  rivet  is  on  a  conical  surface,  and  the  sharp  cutting  edge  of  the  plate 
tends  to  cut  the  rivet  at  the  junction  of  the  head  and  the  shank.  How- 
ever, the  bearing  area  is  increased  and  the  bearing  on  the  sloping  sur- 
face causes  transverse  components  which  tend  to  increase  the  friction 
between  the  parts  connected.  It  seems  as  if  the  minimum  allowance 
of  one-half  value  is  justified.  As  the  thickness  of  the  plate  increases, 
part  of  the  plate  bears  upon  the  rivet  shank,  and  the  value  of  the  rivet 
increases.  When  the  plate  thickness  equals  nine-tenths  of  the  diameter 
of  the  rivet,  the  bearing  value  on  the  shank  alone  equals  the  single  shear 
value  of  the  rivet,  and  there  is  no  question  but  what  the  full  rivet  value 


may  be  counted.    Rivets  should  be  countersunk  only  where  unavoidable 
because  of  their  expense  and  their  uncertain  value. 

1.  Indirect  Riveting.  —  The  number  of  rivets  required  to  transmit  a 
given  stress  should  be  increased  50  %  if  loose  fillers  are  inserted  between 
the  connected  parts.    This  is  discussed  more  fully  on  page  235  : 2.    Simi- 
larly, when  splice  plates  are  not  in  direct  contact  with  the  parts  spliced, 
the  number  of  rivets  should  be  increased  33J  %  for  each  intervening  part. 

2.  Typical  riveted  connections  are  designed  in  the  following  chapters. 
On  account  of  the  inaccuracies  in  the  usual  shop  work,  it  is  not  wise  to 
combine  two  different  types  of  connection.    For  example,  a  girder  may 
be  supported  by  seats  or  brackets,  or  else  by  web  connection  angles, 
but  either  one  or  the  other  should  be  designed  to  carry  the  full  load. 
A  small  erection  seat  may  be  furnished  to  support  the  girder  until  the 
rivets  are  driven  in  the  web  connection  angles,  but  the  strength  of  the 
latter  should  not  be  reduced  as  a  result,  because  it  would  be  difficult  to 
insure  both  connections  acting  simultaneously. 


CHAPTER  XXXV 
RIVETS  IN  TYPICAL  CONNECTIONS 

SYNOPSIS:  The  principles  of  the  preceding  chapter  are  illustrated  by  the  deter- 
mination of  the  number  of  rivets  in  a  few  simple  connections.  Further  application 
of  the  principles  are  shown  in  subsequent  chapters. 


1.  In  the  preceding  chapter  were  presented  the  principles  involved 
in  the  design  of  riveted  joints.     The  application  of  these  principles  will 
now  be  shown  by  typical  riveted  connections. 

2.  Gusset  Plate  — •  Continuous  Chord.  —  This  method   of  connecting 
the  members  of  trusses,  latticed  girders,  bracing,  etc.,  is  very  common, 
as  shown  by  the  typical  drawings  of  Part  II.    The  plates  of  a  truss  are 
usually  made  of  uniform  thickness  unless  it  seems  desirable  to  increase 
the  thickness  of  a  few  of  the  more  important  plates  in  order  to  reduce 
their  size  by  reducing  the  number  of  rivets  required.    Gusset  plates  are 
usually  from  -fg"  to  f "  thick,  T\  and  f  being  commonly  used  except  for 
bridge  trusses  or  other  heavy  work.    Any  cross  section  of  the  plate  must 
have  sufficient  area  to  carry  the  maximum  stress  which  may  come  on 
the  plate  at  that  section.     This  is  largely  a  matter  of  judgment  rather 
than  actual  design  in  most  cases.     For  illustration,  let  us  consider  the 
plate  at  panel  point  K  of  the  roof  truss  of  Fig.  116.    The  number  of  rivets 
in  the  web  members  are  determined  by  the  corresponding  stresses,  pro- 
vided no  less  than  two  rivets  are  used  at  the  end  of  any  member  (page 
228:1).    These  rivets  usually  determine  the  size  of  the  plate  (page  76  : 1). 
The  number  of  rivets  in  the  continuous  chord  is  usually  fixed  by  the 
practical  rules  for  spacing,  so  that  the  edge  distances  will  not  be  exces- 
sive and  so  that  the  distance  between  rivets  will  not  exceed  6".    These 
rivets  do  not  need  to  transmit  the  chord  stress  in  the  panel  on  either  side 
of  the  joint,  but  merely  the  difference  between  these  stresses.    The  con- 
tinuous chord  angles  transmit  the  smaller  stress  from  one  panel  to  the 


4S 


next.  The  stresses  (in  thousands)  for  which  this  joint  is  designed  are 
shown  in  Fig.  233.  Each  web  member  is  composed  of  only  one  angle, 
so  the  rivets  are  in  single  shear.  The  limiting  thickness  of  metal  is  -fg", 
the  angles  and  the  plate  being  the  same.  From  the  table  at  the  top  of 
page  309  we  find  that  the  single  shear  value  of  a  f"  shop  rivet  (5.3 
thousand  pounds)  is  less  than  the  bearing  value  in  a  -f$"  plate  (5.6)  so 
the  former  must  be  used.  By  following  this  column  in  the  table  until 
a  value  is  found  which  equals  or  exceeds 
the  required  stress,  the  corresponding 
number  of  rivets  is  determined.  A  single 
rivet  would  carry  the  smaller  stress  but  a 
minimum  of  two  would  be  used.  Two 
rivets  are  also  sufficient  in  the  other  mem- 
ber. The  chord  is  composed  of  two  angles,  and  the  plate  "is  inserted  be- 
tween them.  The  rivets  are  therefore  in  double  shear  and  the  limiting 
value  is  the  bearing  value  in  the  -fg"  plate,  the  plate  being  thinner  than 
the  combined  thickness  of  the  angles.  Two  rivets  would  carry  the  increase 
in  stress  (7  =  52  -  45)  but  for  practical  reasons  three  are  used. 

3.  Gusset  Plate  —  Spliced  Chord.  —  Where  the  chord  is  not  con- 
tinuous, provision  must  be  made  to  transmit  the  full  stress  in  each 
member.  A  stress  which  is  not  too  large  may  be  transmitted  to  the 
gusset  plate  by  rivets  in  one  leg  only.  Whenever  the  number  of  rivets 
exceeds  about  8,  it  is  well  to  connect  both  legs  if  practical.  The  out- 
standing leg  may  be  connected  to  the  gusset  plate  by  means  of  a  small 


Fig.  233. 


234 


PART  III  — THE  DESIGN  OF  DETAILS 


connection  angle,  as  for  example  at  the  left  end  of  the  chord  angles  of 
the  preceding  problem.  The  outstanding  legs  of  two  adjacent  chord 
members  may  be  connected  by  means  of  a  splice  plate  which  transmits 
part  of  the  stress  directly  from  one  member  to  the  other.  Often  a  plate 
designed  for  another  purpose  may  be  utilized  as  a  splice  plate.  For  ex- 
ample, let  us  consider  the  joint  at  panel  point  H  of  the  roof  truss  referred 
to  in  the  preceding  paragraph.  Each  member  is  composed  of  two  angles, 
and  the  gusset  plate  is  placed  between  them.  All  rivets  in  the  gusset 
plate  are  therefore  in  double  shear,  and  in  value  they  are  limited  by  the 
bearing  in  a  TV  plate.  From  the  table  at  the  top  of  page  309,  two 
shop  rivets  are  found  sufficient  for  the  stresses  in  each  of  the  two  left- 
hand  web  members  (Fig.  116),  but  four  are  required  in  the  right-hand 
member.  The  two  chord  members  are  so  arranged  that  the  outstanding 
legs  may  be  connected  by  means  of  a  splice  plate.  The  proportion  of 
the  stress  to  be  taken  by  the  rivets  in  the  different  legs  depends  upon 
the  special  requirements  of  each  problem.  It  may  be  desirable  to  pro- 
portion the  rivets  approximately  to  the  relative  areas  of  the  angle  legs. 
There  must  be  at  least  enough  rivets  in  the  gusset  plate  to  prevent  the 
web  members  from  moving  the  plate  along  the  chord.  This  tendency  is 
measured  by  the  difference  in  the  chord  stresses,  as  in  the  preceding 
problem.  Unlike  the  gusset  plate,  the  splice  plate  serves  simply  to 
transmit  stress  from  one  chord  member  to  the  other  and  nothing  is 
gained  in  making  one-half  the  splice  stronger  than  the  other  half.  If 
shop  rivets  are  used  in  one-half  and  field  rivets  in  the  other,  or  if  different 
numbers  of  rivets  are  used,  the  stress  cannot  exceed  the  strength  of  the 
weaker  half.  TTiis  should  be  borne  in  mind  when  a  plate  used  for  another 
purpose  serves  as  a  splice  plate.  In  this  problem,  for  example,  a  plate 
in  the  system  of  bottom  chord  bracing  (Fig.  140)  is  so  used,  but  the 
holes  are  not  symmetrical  about  the  joint.  Only  four  rivets  can  be 
counted  upon  to  transmit  the  chord  stress,  because  there  are  only  four 
in  the  right-hand  member.  From  the  table,  four  field  rivets  in  single 
shear  are  worth  18  thousand  pounds.  The  number  of  shop  rivets  bear- 
ing in  the  TV  gusset  plate  required  to  carry  the  remaining  stress  of 
27  =  45  —  18  in  the  left-hand  chord  member  is  5.  Similarly,  the  number 
of  field  rivets  required  in  the  right-hand  member  to  carry  12  =  30  -  18 
is  3 


1.  Symmetrical  Gusset  Plate. — -In  order  to  make   connecting  parts 
alike,  or  symmetrical  about  a  reference  line,  the  same  number  of  rivets 
must  be  used  in  both  parts  even  though  some  of  the  rivets  are  driven 
in  the  shop  and  the  rest  in  the  field.     For  example  only  one-half  of  a 
symmetrical  roof  truss  is  drawn,  and  both  halves  of  the  truss  are  made 
from  the  drawing,  whether  the  truss  is  fully  riveted  in  the  shop  or  shipped 
in  sections.     In  the  latter  case  the  central  peak  plate  (panel  point  F, 
Fig.  116)  is  usually  riveted  in  the  shop  to  one  section  in  order  to  reduce 
the  number  of  field  rivets.    Since  it  is  impractical  to  make  the  plate  un- 
symmetrical,  the  number  of  rivets  must  be  determined  by  the  value  of 
the  field  rivets. 

2.  Web    Connection   for   Beams.  —  Standard    connection    angles    are 
often  used  for  supporting  I-beams  and  channels  under  average  condi- 
tions of  loading.    Their  use  not  only  simplifies  the  drafting  and  the  shop 
work  but  reduces  the  number  of   connections   to  be  designed.     These 
angles  must  not  be  used  blindly  for  all  conditions,  such  as  for  very  short 
spans  or  for  heavy  concentrated  loads.    Draftsmen  soon  become  familiar 
with  the  limitations  of  standard  connection  angles.     All  doubtful  cases 
should  be  investigated,  and  special  connections  should  be  designed  when- 
ever necessary.     Four-inch  legs  are  used  as  a  rule  when  the  rivets  may 
be  put  in  a  single  line,  and  six-inch  legs  for  double  lines.     Thicknesses 
°f  f"j  A"  and  \"  are  used.     The  lengths  depend  upon  the  number  of 
rivets.    Angles  are  regularly  used  in  pairs  except  in  crowded  places  where 
single  angles  may  be  used.     The  shop  rivets  which  connect  the  angles 
to  the  supported  beam  are  accordingly  in  double  or  single  shear.    They 
must  transmit  the  maximum  end  reaction.*    The  field  rivets  which  con- 
nect the  angles  to  the  supporting  member  must  transmit  the  same  maxi- 
mum reaction,  acting  in  single  shear.     If  another  beam  is  connected  to 
the  web  of  the  supporting  member  by  means  of  the  same  field  rivets, 
the  rivets  must  also  transmit  the  combined  reactions  of  the  beamsi  acting 
in  double  shear.     Enough  rivets  must  be  used  to  satisfy  either  of  these 

*  These  rivets  are  sometimes  figured  according  to  the  method  of  eccentric  con- 
nections (next  chapter),  but  ordinarily  this  is  not  done  because  it  is  considered  that 
the  tension  in  the  rivets  through  the  outstanding  legs  will  restrain  the  connection 
angles  sufficiently  to  overcome  the  effects  of  eccentricity.  In  fact  the  tendency  is  to 
use  fewer  rivets  rather  than  more  on  account  of  the  friction  (page  228  :  4) . 


CHAPTER   XXXV 


RIVETS  IN   TYPICAL  CONNECTIONS 


235 


requirements.  The  maximum  number  will  usually  be  required  when 
both  beams  are  loaded,  but  not  always.  (Compare  page  235:  2)  For 
example,  let  us  find  the  number  of  f  "  rivets  required  in  the  two  angles 
connecting  a  15"  I  42#  to  a  T%"  girder  web.  The  beam  is  10'  0"  long, 
and  supports  a  total  load  of  6000#/ft.,  including  its  own  weight.  The 
rivet  values  given  in  the  bottom  table  of  page  309  are  specified.  The 
maximum  reaction  is  30,000#  =  6000  x  5.  The  shop  rivets  are  in  double 
shear,  being  limited  by  the  bearing  value  in  the  f  "  web  (page  322)  of 
the  I-beam.  The  number  of  shop  rivets  required  is  found  from  the  table 
to  be  6.  The  number  of  field  rivets  in  the  outstanding  legs  is  determined 
by  the  single  shear  value  to  be  9,  but  5  would  be  used  in  each  angle  to 
make  them  alike.  If  another  beam  of  the  same  size  and  with  the  same 
load  is  to  be  connected  to  the  opposite  side  of  the  girder  web  by  the  same 
field  rivets,  the  rivets  must  be  proportioned  for  the  combined  load  of 
60,000#.  In  this  case  the  rivets  would  be  in  double  shear  and  limited 
by  the  bearing  in  the  TV  web.  The  number  required  would  thus  be 
increased  from  9  to  16. 

1 .  Seat  Connection  for  Beams.  —  A  seat  angle  is  used  to  support  the 
lighter  beams  of  office  buildings,  as  shown  in  Fig.  89  (a),  (6).  The  beams 
are  held  in  place  by  small  top  or  side  angles,  but  the  seat  angles  are  de- 
signed to  take  the  whole  load.  The  thickness  of  the  seat  angle  is  increased 
with  the  load  in  order  to  prevent  bending,  \"  being  used  for  loads  up  to 
12,000#,  |"  up  to  15,000#,  and  f"  up  to  18,000#.*  For  heavier  loads, 
web  connections  are  preferred  unless  two  beams  have  to  be  supported 
by  the  same  rivets,  in  which  event  seat  angles  with  stiffeners  are  chosen 
on  account  of  erection  (page  89  : 2).  One  or  two  stiffening  angles  may 
be  required,  the  outstanding  legs  being  designed  so  that  the  portion 
outside  the  fillet  of  the  seat  angle  will  carry  the  load  in  bearing  at 
24,000#/sq.  in.  (page  267  : 1).  The  number  of  rivets  in  the  stiffeners 
is  determined  in  the  usual  manner.  Examples  of  this  type  of  connection 
are  shown  in  Figs.  104  and  133.  When  two  stiffeners  are  used  it  is 
not  necessary  to  rivet  their  outstanding  legs  together  unless  exposed 
to  the  weather.  When  the  gage  in  a  single  stiffening  angle  exceeds  1\" 
or  3",  the  connection  should  be  tested  for  eccentricity  (page  237:3). 
For  example,  let  us  find  the  number  of  f "  rivets  required  to  connect  a 
*  Standards  of  the  American  Bridge  Company. 


seat  angle  to  a  Ty  girder  web  to  support  the  end  of  a  12"  I  31|#,  the 
reaction  being  12,000#.  From  the  second  table  on  page  309  we  find 
that  3  shop  rivets  are  required.  If  a  similar  beam  seat  must  be  provided 
on  the  opposite  side  of  the  web,  the  combined  load  will  be  24,000#  and 
the  rivets  will  be  in  double  shear.  Using  the  bearing  value  in  the  web 
we  find  that  4  rivets  are  required. 

2.  Stringer  Connection.  —  The  connection  of  a  stringer  to  the  floor 
beam  of  a  railroad  bridge  may  be  illustrated  by  the  use  of  the  data  given 
on  page  225  :  1.  A  similar  stringer  is  detailed  in  Fig.  98,  and  the  cor- 
responding floor  beam  in  Fig.  99.  The  maximum  end  shear  due  to  live 
load  is  60,000#,  found  by  placing  wheel  2  at  the  extreme  end  of  the  15-ft 

300 
stringer.     This  must  be  increased  by  ^-=  per  cent  for  impact,  and  by 


the  dead  load  of  the  track  and  the  stringer,  thus:    119,900#  =  60,000 

fil  ^  ' 

X  57=  +  (225  +  150)7.5  =  the  maximum  total  end  shear.    The  number 

OlO 

of  shop  rivets  which  connect  the  angles  to  the  stringer  web  is  determined 
from  this  maximum  shear.  The  field  rivets  which  connect  the  angles  to 
the  floor-beam  web  must  resist  either  this  maximum  end  shear  (acting 
in  single  shear),  or  else  the  maximum  load  from  two  stringers  (acting  in 
double  shear).  Either  condition  may  give  the  larger  number  of  rivets 
so  both  must  be  considered.  This  is  because  the  combined  load  or  floor- 
beam  reaction  for  moving  concentrated  loads  can  never  be  twice  the 
maximum  end  shear.  The  maximum  floor-beam  reaction  due  to  the 
live  load  was  found  on  page  194  :  2  to  be  82,000#.  Since  this  is  obtained 

300 
when  two  panels  are  loaded,  the  impact  percentage  is  ^..     The  total 


82,000  x         +  (225  +  150)15. 


floor-beam  reaction  is  therefore  162,200# 

Using  the  first  table  on  page  310,  the  number  of  I"  shop  rivets  bearing 
in  the  f"  stringer  web  required  to  carry  119,900#  is  10.  Rivets  which 
pass  through  fillers  are  less  effective  than  those  which  connect  the  parts 
directly  without  intervening  fillers.  The  common  clause  in  the  speci- 
fications requires  that  the  number  of  rivets  should  be  increased  50% 
if  they  pass  through  fillers.  These  extra  rivets  may  be  used  to  connect 
the  fillers  to  the  web  without  passing  through  the  angles;  in  fact  it  is 


236 


PART   III  — THE   DESIGN   OF  DETAILS 


preferable  to  so  place  them  wherever  practical.  The  total  number  of 
rivets  required  to  connect  the  angles  and  fillers  to  the  stringer  web  is 
therefore  15,  at  least  10  of  which  should  pass  through  the  angles.  The 
rivets  which  pass  through  the  flange  angles  should  not  be  counted  be- 
cause they  will  be  fully  developed  in  transmitting  the  flange  stress.  The 
number  of  field  rivets  in  single  shear  required  to  carry  119,900#  is  20 
while  the  number  bearing  in  a  T7^"  floor-beam  web  required  to  carry 
162,200#  is  22.  If  the  relative  depths  of  stringer  and  floor  beam  necessi- 
tates the  use  of  fillers  between  the  connection  angles  and  the  floor-beam 
web,  as  in  Fig.  99,  the  number  would  be  increased  50%  to  33.  Most 
of  the  extra  rivets  may  be  placed  outside  of  the  angles  or  else  be  counter- 
sunk beneath  them,  thus  holding  the  fillers  in  position  and  minimizing 
the  number  of  field  rivets.  When  shop  rivets  are  thus  substituted  for 
field  rivets  a  corresponding  reduction  in  number  may  be  made. 

1.  Floor-beam   Connection.  —  In   the   alternate   form   of   connection 
shown  in  Fig.  99,  the  floor  beam  is  connected  to  the  stiffening  angles  of 


the  girder  by  means  of  a  gusset  plate.  If  this  plate  is  placed  between 
two  stiffening  angles,  the  rivets  are  in  double  shear  and  usually  limited 
by  the  bearing  value  in  the  plate.  If  only  one  angle  is  used  the  rivets 
are  in  single  shear.  The  total  reaction  at  the  end  of  the  floor  beam  of 
the  preceding  problem  would  be  equal  to  one-half  the  total  load,  or  the 
load  at  one  stringer  point  plus  one-half  the  weight  of  the  floor  beam,  thus: 
163,500#  =  162,200  +  175  x  7.25. 

The  discrepancy  between  this  value  and  the  panel  load  on  the  girder  designed 
on  page  225  :  1  is  due  to  the  different  loaded  lengths  which  determine  the  impact 
percentages. 

2.  Other  Connections.  —  The  rivets  in  eccentric  connections  are 
discussed  in  the  following  chapter;  those  in  the  flanges  of  plate  girders 
in  Chapter  XXXVII,  page  241;  in  the  cover  plates  of  plate  girders, 
Chapter  XXXVIII,  page  259;  in  stiffening  angles,  Chapter  XXXIX,  page 
266;  in  splices,  Chapter  XL,  page  270;  in  reinforcing  plates,  Chapt 
XLII,  page  284;  and  in  column  bases,  Chapter  XLIII,  page  288. 


CHAPTER  XXXVI 
RIVETS  IN  ECCENTRIC  CONNECTIONS 

SYNOPSIS:    The  determination  of  the  number  of  rivets  required  to  resist  the  tend- 
ency of  a  connection  to  rotate,  as  well  as  to  resist  the  direct  stress. 

1.   Definition.  —  Whenever    practicable    the    rivets    in    a    connection     quent  trials.     Naturally,  the  number  first  assumed  should  be  greater 
should  be  arranged  symmetrically  about  the  line  of  action  of  the  resultant     than  the  number  which  would  be  required  to  carry  simply  the  load  if 


force  so  that  the  rivets  on  one  side  balance  those  on  the  other  and  over- 
come any  tendency  of  the  connection  to  twist.  The  rivets  may  then  be 
considered  to  resist  the  direct  shearing  forces  only,  as  in  the  connections 
of  the  preceding  chapter.  If  the  rivets  are  unsymmetrically  placed, 
particularly  if  all  the  rivets  are  on  one  side  of  the  force  or  forces  to  be 
resisted,  the  connection  is  said  to  be  "  eccentric,"  and  special  attention 
must  be  given  to  its  design.  The  tendency  of  an  eccentric  connection 
to  rotate  is  often  so  great  that  the  stresses  on  the  rivets  due  to  moment 
are  larger  than  those  due  to  the  direct  load. 

2.  The  commonly  accepted  method  of  designing  an  eccentric  connec- 
tion is  based  upon  assumptions  which  have  proved  satisfactory  under 
usual  conditions  even  though  they  may  not  be  applicable  to  extreme 
cases.  Formulas,  tables,  and  diagrams  have  been  devised  to  facilitate 
the  design,  but  only  in  special  cases  *  have  they  proved  distinctly  more 
satisfactory  than  the  more  general  method  of  finding  the  number  of 
rivets  by  trial.  The  number  and  the  spacing  of  the  rivets  in  an  eccentric 
connection  are  assumed  and  then  the  efficiency  of  the  whole  connection 
is  investigated.  The  number  depends  not  only  upon  the  load  and  the 
limiting  value  of  each  rivet,  but  also  upon  the  spacing  of  the  rivets  and 
the  amount  of  the  eccentricity.  No  rule  can  be  given  to  aid  the  designer 
in  making  his  first  assumption,  but  each  trial  serves  as  a  guide  for  subse- 

*  See  diagrams  of  F.  W.  Seidensticker  in  Engineering  News-Record  of  June  19, 
1919. 


237 


the  connection  were  concentric.    The  number  of  trials  required  depends 
largely   upon    the    experience    and    the 
judgment  of  the  designer. 

3.  The  application  of  the  method  of 
investigating  the  strength  of  an  eccentric 
connection  by  means  of  a  working  rule 
is  comparatively  simple,  but  the  under- 
lying theory  is  more  complex.  A  typical 
connection  is  shown  in  Fig.  237,  in  which 
0  is  the  center  of  gravity  of  the  group 
of  rivets,  P  is  the  resultant  force  which 
tends  to  cause  rotation  of  the  plate,  and 
e  is  the  eccentricity  or  the  perpendicular 
distance  from  0  to  the  line  of  action  of 
P.  The  rivets  are  not  all  equally  effec- 
tive in  resisting  rotation,  for  those  that 
are  farthest  from  the  center  of  rotation 
are  worth  most  while  those  near  this 
center  are  worth  comparatively  little. 

The  stresses  in  the  rivets  are  proportional  to  the  distances  from  the  rivets 
to  the  center  of  rotation,  and  they  act  in  lines  normal  to  lines  drawn  from 
the  rivets  to  this  center.  If  the  rivets  resisted  simply  the  rotation,  the 
center  of  rotation  would  be  at  0,  the  lines  of  action  of  typical  rivets  being 


Fig.  237. 


238 


PART   III  — THE   DESIGN   OF  DETAILS 


represented  by  the  dashed  lines  in  the  figure.  Usually,  however,  each 
rivet  must  also  support  its  share  of  the  direct  load.  The  effect  of  this  is 
to  increase  the  vertical  component  of  the  stress  in  each  rivet  by  a  con- 
stant amount  (Ek)  and  to  change  the  center  of  rotation  to  0'  on  a  line 
drawn  through  0  perpendicular  to  the  line  of  action  of  the  force  P.  The 
combined  stress  (Ez)  on  any  rivet  acts  in  a  line  normal  to  a  line  drawn 
from  the  rivet  to  the  center  of  rotation  0'.  The  rivet  which  is  farthest 
from  the  center  of  rotation  0'  has  the  largest  combined  stress  (Ezm) 
and  it  is  therefore  the  critical  rivet  in  determining  the  strength  of  the 
connection,  inasmuch  as  its  stress  must  not  exceed  the  limiting  value 
of  a  rivet  under  the  given  conditions  (page  231  : 1).  In  order  to  derive 
the  expressions  used  as  a  basis  for  a  working  rule,  let  us  refer  our  rectangu- 
lar coordinates  to  the  center  of  gravity  of  the  group  of  rivets,  and  our 
polar  coordinates  to  the  center  of  rotation. 

0  =  the  center  of  gravity  of  the  group  of  rivets 

0'  =  the  center  of  rotation 

P  =  the  resultant  force  to  be  resisted 

e  =  the  eccentricity,  or  the  perpendicular  distance  from  0  to  P 
k  =  the  distance  from  0  to  0' 
x  =  the  horizontal  distance  from  0  to  any  rivet 
y  =  the  vertical  distance  from  0  to  any  rivet 
z  =  the  direct  distance  from  0'  (not  0)  to  any  rivet 

zm  =  the  maximum  value  of  z 
xm  and  ym  =  the  values  of  x  and  y  which  correspond  to  zm 

E  =  the  resultant  stress  on  a  rivet  at  unit  distance  from  0' 

N  =  the  number  of  rivets  in  the  whole  connection. 

Since  the  stress  in  any  rivet  is  proportional  to  the  distance  from  the 
rivet  to  the  center  of  rotation  0',  the  resultant  stress  in  a  rivet  at  distance 
z  is  Ez,  and  its  moment  about  0'  is  Ez2.  Frorh  the  figure,  z2  =  (k  ±  a;)2  +  yz. 
By  similar  triangles,  since  E  is  constant,  the  horizontal  component  of 
Ez  is  Ey,  and  the  vertical  component  is  composed  of  two  parts  added 

algebraically,  viz.:    Ex  due  to  rotation,  and  Ek  due  to  the  direct  load. 

p 
Since  E  and  k  are  both  constant,  Ek  is  the  same  for  all  rivets  and  Ek  =  •=; 

also  2Ek  =  P,  and  2Ek*  =  Pk.    In  order  to  satisfy  the  moment  equation 


of  equilibrium,  the  total  resisting  moment  of  the  rivets  must  equal  the 
moment  of  the  force  P  about  0',  or  2&2  =  £  E  [(/e  ±  x)'2  +  y2]  =  P(k+e), 
whence 

22Ekx  +  ZEx2  +  ZEy*  =  Pk  +  Pe. 


Since  0  is  at  the  center  of  gravity  of  the  rivets,  2a;  =  0,  hence  22Ekx  =  0. 
Substituting  this  value  and  2£fc2  =  Pk,  we  have 


+  I,  Eif  =  Pe,        or 


E 


Pe 


The  maximum  resultant  stress  (Ezm)  will  occur  in  the  rivet  which  is 
at  the  maximum  distance  (zm)  from  the  center  of  rotation  (0').  For  this 
rivet  the  Ek  and  the  Exm  of  the  vertical  component  are  combined  because 
they  have  the  same  sign.  From  the  figure,  (Ezm)2  =  (Ek  +  Exm)2  +  (Eym)2, 
from  which  the  maximum  stress  on  the  critical  rivet 


Ezm  - 


+  Exa 


+ 


This  maximum  stress  must  not  exceed  the  limiting  value  of  one  rivet 
as  determined  in  the  usual  manner. 

1.  The  method  derived  in  the  preceding  paragraph  for  investigating 
the  strength  of  the  rivets  in  an  eccentric  connection  may  be  summarized 
in  the  form  of  a  more  convenient  working  rule  as  follows: 

Assume  the  number  and  the  spacing  of  the  rivets  and  find  the 
center  of  gravity  (0)  of  the  whole  group.  Find  E  (or  an  expres- 
sion for  E)  by  dividing  the  moment  (Pe)  of  the  resultant  force 
P  about  0  by  the  sum  of  the  squares  of  the  horizontal  and  the 
vertical  distances  (2x2  +  2z/2)  from  0  to  each  rivet.  Select  the 
rivet  which  is  at  the  maximum  distance  (zm)  from  the  center  of 
rotation  (0')  as  the  critical  rivet.  The  product  of  E  and  the 
vertical  distance  (ym)  from  0  to  the  critical  rivet  is  the  hori- 
zontal component  (Eym)  of  the  maximum  stress  (Ezm).  The 

vertical  component  (TR  +  Exm\  is  found  by  adding  the  direct 

/  P\ 
load  on  each  rivet  ( •=-,']  to   the   product   of   E  and   the    hori- 

\N/ 

zontal  distance  (zm)  from  0  to  the  critical  rivet.    The. resultant 


CHAPTER   XXXVI 


RIVETS   IN   ECCENTRIC   CONNECTIONS 


239 


of  these  two  components  is  the  maximum  stress  on  the  critical 
rivet  (Ezm),  and  this  should  not  exceed  the  limiting  value  allowed 
on  a  single  rivet. 

The  spacing  of  the  rivets  is  often  predetermined  by  existing  conditions. 
The  number  of  rivets  required  is  smaller  when  they  are  spaced  farther 
apart,  but  it  is  impractical  to  exceed  certain  limits  lest  the  resulting 
plate  appear  too  large.  The  position  of  the  center  of  gravity  can  usually 
be  found  by  inspection.  The  sum  of  the  squares  may  be  found  'most 
readily  by  combining  rivets  which  have  equal  values  of  x  or  of  y,  and 
by  using  a  table  of  squares  or  a  slide  rule.  The  resultant  stress  (Ezm) 
may  be  found  graphically  or  by  means  of  the  diagram  on  page  312 
quite  as  conveniently  as  with  the  table  of  squares.  The  limiting  value  of 
one  rivet  depends  upon  the  unit  stress,  the  diameter,  and  whether  the 
rivets  are  in  single  or  double  shear,  as  in  the  preceding  chapters.  See 
page  231  : 1.  In  case  the  connection  proves  not  strong  enough,  rivets 
may  be  added  or  the  spacing  may  be  increased,  whichever  seems  better 
adapted  to  the  specific  problem.  Often  two  or  more  rivets  must  be  added 
to  preserve  the  symmetry  even  though  one  would  give  the  desired  in- 
crease in  strength.  In  like  manner  the  connection  may  prove  to  be  so 
strong  that  the  number  or  the  spacing  of  the  rivets  may  be  reduced. 

1.  The  application  of  the  foregoing  rule  is  illustrated  by  the  following 
typical  problems.  When  the  moment  due  to  the  eccentricity  is  resisted 
by  more  than  one  group  of  rivets,  each  group  is  de- 
signed for  its  portion,  as  illustrated  in  the  design  of 
the  web  splices  of  plate  girders  on  pages  271  : 1  and 
272  : 2. 

First  Problem.  —  Find  the  number  of  \"  shop  rivets 
in  single  shear  at  10,000#/sq.  in.,  spaced  4"  c.  to  c. 
in  two  rows  5|"  apart,  which  are  required  to  support 
an  eccentric  load   of   15,000#,  acting   10"  from  the 
center  of  the  group  of  rivets.    The  value  of  one  rivet 
is  4420  and  four  rivets  would  be  required  to  take  the 
direct  load.     On  account  of  the  comparatively  large 
eccentricity,  we  will  assume  10  rivets  as  shown  in  Fig.  239  (a).     The  center 
gravity  is  midway  between  the  two  central  rivets.     The  value  of  x 


Fig.  239  (a). 


is  2|"  for  each  rivet,  and  the  value  of  y  for  the  center  rivets  is  0,  for 
the  four  outer  rivets  is  8",  and  for  the  four  remaining  rivets  is  4".  The 
sum  of  the  squares  is 


396  =  10  x  2J2  +  4(42  +  82),        and 


E 


15,000  x  10 
396 


The  value  of  E  need  not  be  recorded  if  a  slide  rule  is  used,  for  without 
changing  the  slide,  the  value  of  E  may  be  multiplied  by  ym  =  8,  and 
xm  =  2|  to  give  3030  and  1040  respectively.  The  former  is  the  horizontal 
component  of  the  stress  on  the  extreme  rivet  and  the  vertical  component 
15,000 


is  2540 


10 


+  1040.     The  resultant  of  these  two  is  3950,   which 


is  considerably  under  the  allowed  value  of  4420.    If  we  remove  two  rivets, 
the  strength  of  the  eight  remaining  ones  would  be  found  as  follows: 


220  =  8  x  2f2  +  4(22  +  62)        and        E  = 


15,000  x  10 
220 


Ex&  =  4090,  and   E  x 2f  =  1880.      The   resultant  of    4090    and    3750 
i  fx  nru~i 

— h  1880  is  5550  which  is  much  too  large.     Often  the  magnitude 

o 

of  one  or  both  components  is  such  that  it  is  unnecessary  to  find  the  re- 
sultant before  discarding  the  trial.    In  this  case  10  rivets  would  be  used 
because  4"  spacing  is  specified  and  it  would  be  imprac- 
ticable to  use  9  rivets  even  though  they  proved  strong 
enough.    If  the  spacing  were  not  fixed  it  might  be  either 
reduced  so  that  a  smaller  plate  could  be  used  with  10 
rivets,  or  else  increased  so  that  8  rivets  would  suffice. 

Second  Problem.  —  Find  the  number  of  f  "  rivets 
required  at  12,000#/sq.  in.  to  connect  the  f"  plate  to 
the  two  vertical  angles  of  the  bracket  shown  in  Fig. 
239  (6).  The  rivets  are  in  double  shear,  and  the  limit- 
ing value  of  each  rivet  is  6750,  the  bearing  value  in  a 
|"  plate.  Let  us  assume  six  rivets  spaced  3"  apart  as  shown.  The  sum 

15,000  X  8 


Fig.  239  (6). 


of  the  squares  is  158  =  2(1£2  +  4£2  +  7|2),  since  x  =  0.     E  = 


158 


which  multiplied  by  1\  gives  5710  for  the  horizontal  component.    The 


240 


PART   III  — THE   DESIGN   OF   DETAILS 


vertical  component  is  simply  2500  =  ^  becauSe  Ex  =  0.    The  result-     meet  the  recluirements-    Let  us  ^  2f  «P*cing.    The  sum  of  the  squar 

6  1^1  nnn  v 


6 
ant  is  6230,  which  is  slightly  under  the  allowed  6750.    One  rivet  cannot 


=  132  '  2(1"  +  4"  + 


The  horizontal  comP°nent  =  626°  = 


be  omitted   because   the    horizontal   component  alone   would    be   8000      X  6|,   which   combined   with   the  vertical   component   of  2500  gives  a 


2(32  +  62) 


The  six  rivets  may  be  placed  closer  together  and  still 


resultant    of 
exactly. 


6740.      This    solution    meets    the    requirements    almost 


CHAPTER  XXXVII 
RIVETS  IN  THE  FLANGES  OF  PLATE  GIRDERS 

SYNOPSIS:  The  rivets  which  fasten  the  flange  angles  to  the  web  plate  of  a  girder 
are  not  spaced  uniformly  but  are  proportioned  according  to  the  variable  flange  stress. 
The  methods  of  finding  the  rivet  pitches  under  different  conditions  are  fully  treated 
in  this  chapter. 


1.  The  term  "  flange  rivets  "  is  usually  interpreted  to  mean  the  rivets 
by  which  the  flange  angles  of  a  plate  girder  are  attached  to  the  web 
plate,  and  it  is  so  used  here.    Technically,  however,  the  term  might  also 
apply  to  the  rivets  which  fasten  the  cover  plates  to  the  flange  angles, 
the  spacing  of  which  is  discussed  in  the  following  chapter,  page  263  : 3. 

2.  The  term  "  rivet  pitch  "  commonly  refers  to  the  longitudinal  spacing 
of  the  rivets  which  hold  the  component  parts  of  a  member  together,  and 
not  of  those  which  connect  one  member  to  another,  although  it  is  some- 
times used  synonymously  with  the  more  general  term  "  rivet  spacing." 
The  pitch  of  the  flange  rivets  in  a  plate  girder  is  the  distance  from  center 
to  center  of  adjacent  rivets  measured  parallel  to  the  longitudinal  axis 
of  the  girder.     If  the  rivets  in  one  flange  are  placed  on  two  lines  they 
are  "  staggered  "  or  alternated,  but  the  pitch  is  the  distance  from  the 
center  of  a  rivet  on  one  line  to  the  center  of  the  next  rivet  on  the  other 
line  measured  not  directly,  but  parallel  to  the  axis  of  the  girder,  as  shown 
in  Fig.  241. 

3.  Since  the  great  majority  of  girders  are  horizontal,  it  is  convenient 
to  speak  of  "  horizontal  "  and  "  vertical  "  stresses  in  the  flanges  for  the 
sake  of  brevity.     This  chapter  may  be  made  to  apply  to  vertical  or 
inclined  girders  by  substituting  for  "  horizontal  "  the  more  general  ex- 
pression  "  parallel   to   the   longitudinal    axis    of   the   girder,"    and   for 
"  vertical  "  the  expression   "  perpendicular  to  the  longitudinal  axis  of 
the  girder." 


4.  There  is  a  demand  for  a  more  complete  treatise  on  the  subject  of 
flange  riveting  than  is  found  in  most  books  on  the  market.  In  this 
chapter  are  given  the  formulas  and  the  methods  used  under  different 
conditions,  and  also  the  proofs  of  the  formulas  and  the  reasons  for  making 
the  different  assumptions.  At  the  end  of  the  chapter  the  different  cases 


Pitch 


O    O    O-  \ 


Fig.  241. 

are  summarized  for  convenient  reference,  but  it  is  recommended  that 
the  summary  be  used  only  after  a  full  understanding  of  the  underlying 
theory  has  been  gained. 

5.   General  Discussion.  —  The  flange  rivets  in  a  girder  are  usually 
spaced  closer  together  near  the  ends  than  near  the  center  because  the 


241 


242 


PART   III  — THE  DESIGN   OF  DETAILS 


rate  of  increase  in  the  flange  stress  near  the  ends  is  greater.  If  a  girder 
is  symmetrical  only  one-half  need  be  considered.  The  maximum  pitches 
at  the  ends  and  at  other  points  are  determined  for  each  girder  by  the 
methods  explained  in  this  chapter.  These  maximum  pitches  are  based 
upon  the  proper  number  of  rivets  required  to  transmit  the  flange  stresses. 
The  spacing  must  also  conform  to  the  general  rules  for  rivet  spacing 
given  in  Chapter  XIII,  page  68,  particularly  regarding  the  maximum 
and  minimum  values.  The  minimum  rivet  pitch  should  not  be  less  than 
the  proper  value  selected  from  the  table  on  page  306.  These  values 
are  determined  by  the  strength  of  the  web  plate  between  rivets,  as  ex- 
plained on  page  255  : 2.  This  is  an  important  consideration  which  is 
too  often  overlooked  by  designers.  The  pitch  in  the  end  panel  of  a  girder 
is  first  determined,  because  if  it  is  found  to  be  less  than  the  minimum 
allowed,  some  change  must  be  made  in  the  design  of  the  flange,  as  for 
example:  (a)  if  the  vertical  legs  of  the  angles  are  less  than  6",  they  may 
be  increased  to  permit  the  staggering  of  the  rivets;  (6)  the  value  of  each 
rivet  may  be  increased  by  increasing  either  the  diameter  of  the  rivet 
or  the  thickness  of  the  web  plate;  (c)  vertical  flange  plates  may  be  inserted 
between  the  angles  and  the  web;  or  (d)  as  a  last  resort  the  depth  of  the 
girder  may  be  increased  or  the  length  of  span  may  be  decreased.  A  con- 
stant pitch  is  used  throughout  a  given  panel  as  explained  later.  The 
pitch  in  each  panel  should  extend  at  least  as  far  as  the  beginning  of  the 
next  panel.  In  spacing  the  rivets  it  may  be  desirable  to  extend  one  pitch 
beyond  its  panel;  the  next  pitch  need  not  then  extend  a  full  panel  pro- 
vided it  extends  as  far  from  the  end  of  the  girder  as  the  point  at  which 
the  next  pitch  is  calculated.  Instead  of  changing  the  pitch  at  the  center 
of  a  concentrated  load  the  smaller  pitch  should  be  extended  past  the  entire 
connection.  Rivets  adjacent  to  stiffening  angles  should  be  placed  far 
enough  away  to  give  driving  clearance,  even  though  the  calculated  pitch 
is  exceeded.  It  is  unnecessary  to  calculate  the  pitch  beyond  the  panel 
where  it  reaches  the  specified  maximum  because  this  maximum  pitch  must 
be  used  from  this  panel  to  the  center.  This  maximum  pitch  never  exceeds 
6",  and  it  is  usually  limited  to  4"  or  \\"  in  crane  runway  girders  and  rail- 
road girders  or  stringers  when  the  loads  rest  directly  upon  the  flanges. 

1.   Some  of  the  controlling  factors  which  determine  the  pitch  of  flange 
rivets  are: 


(a)  the  form  of  loading   (fixed  or  moving,  concentrated  or  uniformly 

distributed) , 
(6)  the  application  of  the  loads  (to  the  web  or  to  the  flange), 

(c)  the  method  of  design  adopted  (whether  the  resisting  moment  of  the 
web  plate  is  considered), 

(d)  the  depth  of  the  girder  between  rivet  lines, 

(e)  the  limiting  value  of  each  rivet, 

(/)  the  general  rules  which  govern  rivet  spacing 
(</)  the  strength  of  the  web  between  rivets. 

2.  Forces  Considered.  —  The  web  plate  of  a  girder  is  designed  to 
resist  all  shearing  stresses,  and  corresponds  to  the  web  members  of  a 
parallel-chord  truss.    It  transfers  vertical  forces  diagonally  to  the  flanges 
which  are  designed  for  horizontal  stresses  like  the  chords  of  a  parallel 
chord  truss.     All  vertical  loads  must  be  transmitted  either  directly  or 
indirectly  to  the  web  plate.     Fixed  concentrated   loads  are  either  con- 
nected directly  to  the  web  or  else  transmitted  to  it  by  means  of  stiffening 
angles.     Uniformly  distributed  loads  and  moving  concentrated  loads  are 
either  applied  directly  to  the  web  through  some  type  of  solid-floor  con- 
struction, or  else  rest  upon  one  of  the  flanges  (usually  the  top).     The 
flange  rivets  must  be  designed  to  transmit  to  the  flange  angles  and  cover 
plates  the  horizontal  stresses  due  to  bending,  and  in  addition  they  must 
transmit  to  the  web  plate  any  vertical  loads  which  rest  on  the  flanges. 
The  rivets  in  any  panel  must  transmit  the  maximum  increase  in  horizontal 
flange  stress  in  that  panel.    It  so  happens  that  this  increase  in  horizontal 
flange  stress  is  equivalent  to  the  vertical  shear  for  a  certain  section,  and 
it  is  convenient  to  make  use  of  this  fact.    No  one  should  receive  the  false 
impression,  however,  that  the  rivets  are  proportioned  for  vertical  forces 
(except  in  part  for  flange  loads).    Moving  loads  should  be  placed  to  give 
the  maximum  shear. 

3.  In  this  chapter  the  depth  used  in  proportioning  the  flange  rivets 
of  a  girder  is  the  perpendicular  distance  between  the  rivet  lines,  and 
not  between  the  centers  of  gravity  of  the  flanges.     When  two  lines  are 
used  in  each  flange,  the  mean  depth  is  taken,  as  shown  in  Fig.  241.    It  is 
logical  to  use  the  depth  between  rivet  lines  because  it  is  the  distance 
between  the  lines  of  action  of  the  stresses  for  which  the  rivets  are  designed. 


CHAPTER   XXXVII 


RIVETS   IN  THE  FLANGES  OF  PLATE  GIRDERS 


243 


The  flange  stresses  can  be  transmitted  from  the  web  to  the  angles  only 
by  means  of  the  rivets  acting  along  these  lines  of  action.  The  resisting 
moment  of  the  stresses  in  the  rivets  is  the  moment  of  a  couple,  equal 
to  the  product  of  the  stress  in  the  rivets  in  either  flange  by  the  perpen- 
dicular distance  between  the  lines  of  action.  This  resisting  moment  must 
be  equal  to  the  resisting  moment  of  the  flanges  and  hence  to  the  cor- 
responding bending  moment.  If  the  depth  between  rivet  lines  is  less 
than  the  depth  used  in  the  design  of  the  flanges,  a  correspondingly  greater 
flange  stress  must  be  resisted  by  the  rivets  than  by  the  angles  and  cover 
plates.  This  is  analogous  to  the  common  method  of  designing  the  web 
splice  plates  which  transmit  the  portion  of  the  bending  stresses  resisted 
by  the  web  plate,  explained  on  page  272  : 2.  It  is  also  consistent  with 
the  design  of  pin-connected  trusses  in  which  the  depth  is  measured  be- 
tween the  centers  of  the  pins  and  not  necessarily  between  the  centers 
of  gravity  of  the  chords.  The  increased  stress  which  results  from  the 
use  of  a  reduced  depth  may  provide  in  some  measure  for  the  secondary 
stresses  which  exist  in  almost  every  girder  due  to  the  fact  that  the  rivets 
are  not  placed  at  the  centers  of  gravity  of  the  flanges.  The  mean  depth 
between  rivet  lines  in  inches  is  denoted  by  dr,  while  in  feet  it  becomes  Dr; 
it  should  usually  be  taken  to  the  nearest  quarter  of  an  inch.  Advocates 
of  the  use  of  other  depths  may  adapt  this  chapter  to  their  needs  by  simply 
substituting  another  depth  for  rfr. 

1.  The  different  conditions  under  which  flange  rivets  are  proportioned 
are  considered  under  eight  different  cases.  For  the  sake  of  simplicity 
in  each  of  the  first  five  cases  it  is  assumed  that  the  girder  is  designed 
according  to  Case  A  (page  221  :  2),  in  which  the  flanges  resist  the  whole 
bending  moment  and  the  resisting  moment  of  the  web  plate  is  neglected. 
Case  VI  shows  how  the  first  five  cases  may  be  modified  when  the  girder 
is  designed  according  to  Case  B  (page  223  :  3),  in  which  the  resisting  mo- 
ment of  the  web  is  considered.  Cases  VII  and  VIH  show  the  applica- 
tion of  the  principles  of  the  foregoing  cases  to  special  girders. 

The  subdivisions  are  as  follows: 

Case  I.    Concentrated  static  loads  applied  to  the  web  (page  243  :2). 
Case  II.     Uniformly  distributed  static  loads  applied  to  the  web   (page 
244  :  2). 


Case  III.    Combined  concentrated  and  uniformly  distributed  static  loads 

applied  to  the  web  (page  246  :  2). 

Case  IV.     Moving  loads  applied  to  the  web  (page  247  : 1). 
Case  V.     Loads  applied  to  the  flange  (page  248  :  2). 
Case  VI.     Girders  in  which  the  web  is  considered  to  resist  part  of  the 

flange  stress  due  to  bending  moment  (page  250  :  2). 
Case  VII.    Box  girders,  cantilever  girders,  and  girders  with  non-parallel 

flanges  (page  252  : 1). 
Case  VIII.     Girders  with  vertical  flange  plates,  and  girders  with  four 

angles  in  each  flange  (page  253  : 1). 
The  determination  of  the  minimum  pitch  based  upon  the  strength  of  the 

web  (page  255  :  2). 
Summary  (page  257). 

CASE   I  —  CONCENTRATED    STATIC    LOADS   APPLIED   TO   THE   WEB 

2.  How  Applied.  —  Concentrated  loads  are  applied  to  plate  girders 
only  in  conjunction  with  uniformly  distributed  loads.     These  uniform 
loads  may  be  due  simply  to  the  weights  of  the  girders  themselves,  or  they 
may  include  other  dead  or  live  loads.     For  the  purpose  of  explanation, 
it  seems  best  to  begin  with  the  discussion  of  the  separate  systems  of  load- 
ing and  to  combine  them  later.     Concentrated  loads  may  be  applied  to 
one  of  the  flanges  as  explained  under  Case  V,  but  under  this  Case  I  are 
considered  only  concentrated  static  loads  which  are  connected  directly 
to  the  web  plate  by  means  of  connection  angles  or  stiffening  angles. 
Concentrated    static   loads  may   be  fixed   in   position   but  variable  in 
magnitude;    the  rivet  pitch  should  be  determined  from  the  maximum 
values. 

3.  Bending  Moment  Theory.  —  The  curve  of  bending  moments  for 
a  system  of  static  concentrated  loads  is  a  series  of  straight  lines,  as  shown 
in  Fig.  189.    The  bending  moment  increases  constantly  from  either  end 
of  a  girder  to  the  point  of  application  of  the  nearest  load,  and  also  from 
one  load  to  another.    The  rivet  pitch  should  therefore  remain  constant 
from  one  load  (or  reaction)  to  the  next  load.    There  should  be  enough 
rivets  between  two  loads  to  satisfy  the  difference  in  flange  stress  between 
their  points  of  application.     Thus  there  will  be  enough  rivets  between 
the  end  of  a  simple  girder  where  the  bending  moment  is  zero,  and  any 


244 


PART   III  — THE   DESIGN   OF   DETAILS 


*•£ 

dr 


other  point  to  carry  the  flange  stress  due  to  the  total  bending  moment 
at  that  point.  It  was  shown  on  page  181 : 1  that  the  increase  in  bending 
moment  between  the  points  of  application  of  fixed  concentrated  loads 
is  equal  to  the  product  of  the  shear  for  a  section  between  the  loads  multi- 
plied by  the  distance  between  the  loads.  If  we  represent  the  vertical 
shear  in  any  panel  by  V,  the  increase  in  bending  moment  in  any  panel 
of  length  B  feet  is  VB,  and  the  corresponding  increase  in  horizontal  flange 

VB 
stress  to  be  taken  by  the  rivets  in  the  panel  is  -yr-  (page  242  :  3).    If  the          CASE  n— UNIFORMLY 

limiting  value  of  one  rivet  under  the  given  conditions  is  r  (usually  the 
bearing  value  in  the  web  plate,  page  230  :  3),  the  number  of  rivets  required 

VB 

in  the  panel   is  — fj-.-s-  f-     These  rivets  are   equally  spaced  throughout 


V 


intensity  of  horizontal  shear  then  becomes  v  =  -=—,  and  the  corresponding 

Clrt 

stress  per  linear  inch  is  found  by  multiplying  by  the  web  thickness  t  to 
Since  the  value  of  each  rivet  is  r,  the  distance  between  rivets 


should  be  r  +  -j-,  or  p-- 


rdr 


as  before. 


DISTRIBUTED    STATIC 
THE    WEB 


LOADS   APPLIED    TO 


is 

the  panel  B,  hence  the  pitch  in  feet  measured  horizontally  from  center 
to  center  of  rivets  is  B  -=-  -yr  or  ~.     Since  the  pitch  is  always   less 

TL/r  V 

than  one  foot  it  should  be  expressed  in  inches,  and  the  above  value  should 
be  multiplied  by  12,  which  changes  Dr  to  dr.    Thus  the  pitch  in  inches  is 


P 


rdr 


1.   Shear  Theory.  —  The  expression  found  in  the  preceding  paragraph 
may  be  derived  also  by  an  entirely  different  method.     The  intensity  of 

Va 

horizontal  shear  at  any  point  of  a  girder  with  fixed  loads  is  v  =  j^  (page 

202  : 1).  Assuming  the  flange  stresses  to  be  concentrated  at  the  rivet  lines 
according  to  page  242 : 3,  and  neglecting  the  resisting  moment  of  the 
web  plate  according  to  Case  A  (page  221:2),  b  =  t  =  the  web  thickness, 

q  =  -=-,   and   /  =  27'  +  2a  f— rj ,  where  a  =  the  area  of  angles  and  cover 


plates  of  one  flange,  and  /'  =  the  corresponding  moment   of  inertia  about 

V  4/' 

an  axis  through  the  rivet  line.     Then  v  =  /A  r, — — .     The  term  — r- 

ddr 


can  with  safety  be  neglected;    it  is  usually  a  small  fraction,  particularly 
at  the  ends  of  the  girder  where  its  effect  would  be  most  pronounced.    The 


2.  How  Applied.  —  The  weight  of  a  girder  is  considered  to  be  uniformly 
distributed  throughout  its  length.    The  superimposed  load  may  be  con- 
centrated, uniformly  distributed,  or  part  concentrated  and  part  uniform. 
The  superimposed  loads  may  be  moving  loads,  as  discussed  under  Case 
IV  (page  247:1),  and  they  may  be  applied  to  the  flange,  as  discussed 
under  Case  V  (page  248  :  2).    Under  this  Case  II  are  considered  only  static 
uniformly  distributed  loads  which  are  applied  to  the  web.     The  weight 
of  the  girder  may  be  included. 

3.  Theory.  —  The   curve   of  bending  moments   for   loads   which   are 
uniformly  distributed  the  full  length  of  a  girder  is  a  parabola.    Since  the 
flange   stress   is   directly   proportional   to   the   bending   moment    (since 
F  =  MB  -5-  Dr),  a  parabola  may  be  drawn  the  ordinates  of  which  repre- 
sent the  flange  stresses  at  different  points,  as  shown  by  the  curved  line  (1) 
in  Fig.  245  (a).    The  flange  stress  is  zero  at  the  ends  of  a  simple  girder,  and 
maximum  at  the  center.     The  rate  of  increase  is  not  constant,  but  is 
greater  near  the  ends,  and  the  rivet  pitch  should  accordingly  be  smaller 
at  the  ends  and  larger  at  the  center.     Theoretically,  no  two  intervals 
should  be  alike,  but  this  is  impractical  because  of  the  amount  of  calcula- 
tion involved  in  determining  the  pitches,  and  because  of  the  extra  work 
required  in  spacing  the  rivets  both  in  the  drafting  room  and  in  the  shop. 
It  is  customary  to  subdivide  the  girders  into  panels,  to  determine  the 
pitch  at  the  beginning  of  each   panel,  and  to  use  this   constant  pitch 
throughout  that  panel,  even  though  more  rivets  are  thus  used  than  are 
theoretically  required.    The  panel  lengths  are  arbitrarily  chosen  approxi- 
mately equal  to  the  depth  of  the  girder,  preferably  equal  to  the  depth 
between  rivet  lines.    It  is  not  necessary  that  the  girder  length  be  an  exact 


CHAPTER   XXXVII 


RIVETS  IN  THE  FLANGES  OF  PLATE   GIRDERS 


245 


multiple  of  the  panel  length  chosen,  the  balance  being  placed  at  the 
center  where  the  same  pitch  usually  extends  for  more  than  one  panel. 
When  intermediate  stiffening  angles  are  used,  the  panel  lengths  may  be 
made  to  conform  to  the  spacing  of  the  stiffeners,  although  if  the  distance 
between  stiffeners  greatly  exceeds  the  girder  depth  an  excessive  number 
of  rivets  will  result.  As  in  the  case  of  concentrated  loads  it  is  convenient 
to  make  use  of  the  relation  between  bending  moment  and  vertical  shear, 
but  for  uniformly  distributed  loads  the  shear  is  not  constant  through- 
out any  panel.  It  may  be  easily  proved  that  the  increase  in  bending 
moment  per  panel  for  fixed  loads  is  equal  to  the  product  of  the  panel 
length  and  the  average  vertical  shear,  i.e.,  the  shear  for  a  section  in  the 
middle  of  the  panel.  The  corresponding  increase  in  horizontal  flange 
stress  is  equal  to  this  product  divided  by  the  depth  Dr.  In  Fig.  245  is 
shown  the  relation  between  the  horizontal  flange  stress  and  the  vertical 
shear.  The  ordinates  in  (a)  represent  the  total  horizontal  flange  stress 
while  those  in  (6)  represent  the  total  vertical  shear.  The  parabola  (1) 
shows  the  actual  flange  stress  due  to  the  full  load,  and  the  straight  line 
(5)  shows  the  actual  shear.  If  the  increase  were  constant  in  any  one 
panel,  the  stress  diagram  would  assume  the  position  of  the  dotted  line  (2) . 
The  corresponding  shear  diagram,  showing  the  constant  average  shear 
per  panel,  is  represented  by  the  stepped  dotted  line  (6).  If  the  rivets 
in  each  panel  were  porportioned  from  this  constant  increase,  it  is  apparent 
from  either  diagram  that  there  would  be  a  deficiency  in  the  first  half  of 
the  panel,  although  this  would  be  made  up  in  the  second  half  so  that  the 
total  number  of  rivets  in  the  panel  would  be  sufficient.  In  order  to 
satisfy  the  increase  in  flange  stress  at  the  beginning  of  the  panel,  however, 
the  rivet  pitch  must  be  determined  from  the  shear  for  a  section  at  the 
beginning  of  the  panel  instead  of  at  the  middle.  In  other  words,  if  a 
constant  pitch  is  used  it  must  not  exceed  the  smallest  pitch  which  would 
be  used  at  the  beginning  of  the  panel  if  the  pitch  were  varied  according 
to  the  actual  stress  curve.  The  effect  of  this  is  shown  graphically  by 
the  heavy  lines  (7)  and  (3)  which  lie  entirely  outside  of  the  theoretical 
lines  (5)  and  (1).  The  excess  in  the  number  of  rivets  when  spaced  uni- 
formly in  this  manner  instead  of  according  to  the  ordinates  of  the  parab- 
ola is  justified  by  the  practical  advantages.*  In  view  of  this  excess, 

TT  7? 

*  This  excess  cannot  exceed  — —  in  any  panel. 


each  rivet  pitch  may  be  taken  to  the  nearest  \" .    The  method  of  solution 
is  much  the  same  as  for  concentrated  loads,  and  the  expression  p  =  -— 

5  Panels  of  B- 


(a) FLANGE  STRESS  DIAGRAM 


(b)  SHEAR  DIAGRAM 
Fig.  245. 


246 


PART   III  — THE   DESIGN   OF   DETAILS 


may  be  derived  in  the  same  manner.  In  the  case  of  uniformly  distributed 
loads  the  V  is  limited  to  the  shear  for  a  section  at  the  beginning  of  the 
panel.  If  the  panels  are  of  equal  length,  the  shears  for  different  sections 
may  be  easily  found  by  means  of  a  constant  difference.  The  application 
of  this  Case  is  shown  by  the  following  illustrative  problem. 

1.  Illustrative      Problem  —  Uniformly    Distributed     Static     Loads.— 
Find  the  rivet  pitches  in  the  18-ft.  girder  designed  on  page  222  : 1,  assum- 
ing that  the  total  load  is  6500#/ft.,  including  the  weight  of  the  girder. 
Use  a  unit  stress  in  bearing  of  24,000#/sq.  in. 

6750#  =  r  =  value  of  one  f"  rivet  bearing  in  a  f"  plate  (page  309) 
19.5"  =  24  J  -  2  x  2|  =  dr  =  depth  between  rivet  lines 
58,500#  =  6500  X  9  =  V  f  or  1st  panel  =  maximum  end  shear 
10,500#  =  6500  x  19.5  -=-  12  decrease  in  shear  per  panel  of  19.5" 
48,000#  =  58,500  -  10,500  =  V  for  2nd  panel 
37,500#  =  48,000  -  10,500  =  V   "   3rd     " 
27,000#  =  37,500  -  10,500  =  V   "   4th      " 

2\"  =  6750  x  19.5  -=-  58,500  =  pitch  in  1st  panel 

2f"  =  6750  x  19. 5 -=-48,000  =     "      "2nd     " 

3£"  =  6750  X  19.5  -f-  37,500  =     "      "  3rd      " 

5"    =  6750  x  19.5  +  27,000  =     "      "  4th      " 

6"    =  maximum  pitch  for  balance. 

In  this  first  problem  each  step  is  clearly  indicated,  but  in  general  the 
solution  can  be  simplified  by  being  arranged  in  tabular  form  as  in  sub- 
sequent problems.  Since  the  pitch  in  the  first  panel  is  not  less  than  the 
minimum  value  2j"  found  in  the  first  table  on  page  306,  the  solution 
is  satisfactory. 

CASE   HI— COMBINED   CONCENTRATED   AND   UNIFORMLY   DISTRIBUTED 
STATIC   LOADS   APPLIED   TO   THE  WEB 

2.  Method.  —  The  rivet  pitches  in  girders  which  support  both  con- 
centrated and  uniformly  distributed  static  loads  are  determined  from 
a  combination  of  the  methods  of  Cases  I  and  II.    The  pitch  for  any  panel 

rdr 
is  found  from  the  formula  p  =  •==-,  in  which  V  is  the  total  shear  for  a  sec- 


tion at  the  beginning  of  the  panel  due  to  the  combined  loads.  If  the 
shear  due  to  the  uniform  load  is  relatively  small,  the  pitch  is  usually 
changed  only  at  the  points  of  concentration.  For  example,  the  floor 
beam  of  a  double-track  through  railroad  bridge  would  support  four  con- 
centrated loads  at  the  stringer  points.  These  concentrated  loads  would 
include  the  live  load,  the  impact,  and  the  dead  load  due  to  the  track  and 
the  stringers.  The  uniformly  distributed  load  would  consist  merely  of 
the  weight  of  the  floor  beam  itself  which  is  so  comparatively  small  that 
the  shear  is  virtually  constant  between  points  of  concentration.  The 
first  pitch  would  be  determined  from  the  total  end  shear  and  used  from 
the  end  to  the  first  stringer.  The  second  pitch  would  be  determined 
from  the  total  shear  for  a  section  just  inside  the  first  concentrated  load 
and  used  from  the  first  to  the  second  stringers.  The  shear  in  the  central 
panel  would  be  so  small  in  this  case  that  the  maximum  pitch  of  6"  would 
be  sufficient.  Again,  if  the  concentrated  loads  are  relatively  small,  the 
change  in,  shear  at  the  points  of  concentration  may  be  negligible,  and  the 
pitch  may  be  changed  only  at  the  panel  points  selected  for  the  uniform 
loads,  although  the  shears  for  sections  at  these  points  must  include  both 
systems  of  loads.  Since  the  rivet  pitch  increases  toward  the  center,  it 
is  safe  to  extend  any  pitch  nearer  the  center  than  is  theoretically  neces- 
sary. When  neither  system  of  loads  predominates,  the  pitch  should  be 
changed  both  at  the  points  of  concentration  and  at  the  panels  of  the  uni- 
form loads.  Each  pitch  is  calculated  at  one  point  from  the  combined 
shear  and  extends  to  the  next  point  where  the  pitch  is  found.  For  ex- 
ample, if  a  concentrated  load  falls  between  panel  points  2  and  3,  the 
pitch  found  at  2  would  be  used  between  2  and  the  load,  but  from  the  load 
to  3  the  pitch  found  from  the  shear  for  a  section  just  to  the  right  of  the 
load  would  be  used.  The  pitch  found  at  3  would  be  used  from  3  to  4 
unless  there  was  another  concentrated  load  between  them,  in  which  case 
the  pitch  would  change  at  the  load  as  before. 

3.  Variable  Fixed  Loads.  —  For  loads  which  are  fixed  in  position  but 
variable  in  magnitude,  the  pitch  in  any  panel  should  be  determined  from 
the  loads  which  cause  a  maximum  shear  in  that  panel.    This  is  illustrated 
by  the  problem  on  page  250  :  3. 

4.  Illustrative    Problem  —  Combined    Loads.  —  Find    the    pitches    o 
the  f "  flange  rivets  in  an  80-ft.  girder  composed  of  an  84  x  -fa"  web 


CHAPTER   XXXVII 


RIVETS 


THE   FLANGES  OF  PLATE  GIRDERS 


247 


6x6  angles,  and  cover  plates.  There  is  a  concentrated  load  of  30,000# 
every  10  feet,  and  a  total  uniformly  distributed  load  of  2000#/ft., 
including  the  weight  of  the  girder.  Use  a  unit  stress  in  bearing  of 
20,000#/sq.  in. 

6560#  =  r  =  value  of  one  f"  rivet  bearing  in  a  TV  plate  (page  309) 
77.25"  =  84}  -  (2  x  2}  +  2})  =  dr 
6'  6"  =  B  =  panel  length,  approximately  equal  to  D, 

The  pitch  changes  at  these  panel  points  and  at  the  points  of  applica- 
tion of  the  concentrated  loads,  as  indicated 
30  in  Fig.  247.    The  first  pitch  is  used  from  the 

•^center     encj  £O  pOjnt  ij  the  next  from  1  to  2,  and 
tes2  the  last  from  5  to  the  center,  being  the  maxi- 

Fig.  247.  mum  allowed  (page  69  : 1). 


30 


123       4*5      S     178 


30 


I  I 


Point 

Shear  -  V 
(in  thousands) 

6.56  X  77.25 

1     itCll                                                                  y 

End 

185.0 

=  30  x  3J  +  2  x  40 

2f 

1 

172.0 

=  185.0  -2  x6| 

3' 

2 

135.0 

=  172.0  -30  -2  x3J 

3f 

3 

129.0 

=  135.0  -2x3 

4' 

4 

116.0 

=  129.0  -2  x6£ 

4i" 

5 

85.0 

=  116.0  -30  -2  x  \ 

6'  max. 

The  first  pitch  is  not  less  than  the  minimum  of  1|£"  found  in  the  bottom 
table  on  page  306  or  the  minimum  of  If"  found  from  the  diagram  on 
page  305  so  the  solution  is  satisfactory. 

CASE   IV  — MOVING   LOADS   APPLIED   TO   THE   WEB 

1.  How  Applied.  —  Moving  loads  may  be  applied  to  the  webs  of  the 
girders  of  a  through  bridge  by  means  of  some  system  of  solid  floor  con- 
struction in  which  the  floor  is  connected  directly  to  the  girder  webs  with- 
out the  use  of  floor  beams. 


2.  Theory.  —  From  the  formula  p  =  -^-  it  is  apparent  that  the  rivet 

pitch  varies  inversely  with  the  shear,  and  is  therefore  minimum  when 
the  shear  is  maximum.  That  this  is  true  may  be  shown  in  two  ways. 
From  the  derivation  of  the  formula  by  the  shear  theory  (page  244 : 1) 
it  is  obvious  that  the  maximum  increase  in  flange  stress  will  be  maximum 
when  the  intensity  of  horizontal  shear  is  maximum,  and  this  will  be  when 
the  vertical  shear  is  maximum.  From  the  derivation  by  the  bending 
moment  theory  (page  243  : 3)  it  is  shown  that  the  increase  in  flange  stress 
is  a  function  of  the  vertical  shear  and  is  therefore  a  maximum  at  the 
same  time.  In  order  to  determine  the  rivet  pitch  at  any  point  in  the 
flange  of  a  girder,  the  moving  loads  should  be  placed  to  cause  a  maximum 
shear  for  a  section  taken  at  that  point.  The  position  of  moving  loads 
which  will  cause  a  maximum  shear  for  any  section  is  explained  on  page 
189  :  3.  The  girder  is  subdivided  into  panels  as  in  Case  II,  page  244  :  2. 
The  effect  of  spacing  the  rivets  according  to  the  maximum  shear  for 
moving  uniformly  distributed  loads  is  shown  graphically  in  Fig.  245.  The 
actual  curve  of  maximum  shear  is  a  parabola  (8)  with  the  vertex  at  the 
support  where  the  shear  is  zero.  The  dot  and  dash  stepped  line  (9)  is 
based  upon  a  constant  shear  in  each  panel  equal  to  the  maximum  shear 
at  the  beginning  of  the  panel.  The  dot  and  dash  line  (4)  shows  the  cor- 
responding flange  stress.  Although  there  is  a  considerable  excess  in 
the  total  number  of  rivets  due  to  the  fact  that  constant  pitches  are  used 
for  practical  reasons,  yet  it  is  essential  that  the  rivets  be  placed  closely 
.enough  at  every  point  to  provide  for  the  maximum  local  stress,  even 
though  not  all  the  remaining  rivets  are  fully  stressed  at  the  same  time. 
The  moving  loads  must  be  placed  in  a  different  position  in  determining 
the  shear  for  the  pitch  in  each  different  panel,  but  the  shear  must  be  the 
total  shear  due  to  both  the  moving  or  "  live  "  loads  with  impact,  and  the 
static  or  "  dead  "  loads.  The  latter  usually  extend  the  entire  length  of 
the  girder  at  all  times. 

3.  Approximate  Method.  —  For  uniformly  distributed  live  loads,  the 
maximum  shear  varies  with  the  square  of  the  distance  from  the  section 
to  the  vertex  of  the  parabola  at  the  further  end  of  the  span,  and  it  is 
convenient  to  find  the  shear  for  the  section  at  the  beginning  of  each  panel 
from  the  maximum  live-load  end  shear  by  proportion  in  this  way.    These 


248 


PART   III  — THE   DESIGN   OF  DETAILS 


shears  may  be  combined  with  the  corresponding  dead-load  shears  to  give 
the  proper  totals.  In  case  the  uniformly  distributed  live  loads  are  rela- 
tively very  large,  as  for  example,  when  there  is  no  other  dead  load  than 
the  weight  of  the  girder,  it  is  usually  sufficiently  close  to  apply  this  ratio 
to  the  combined  live-  and  dead-load  shears.  In  this  case  the  inverse  ratios 
may  be  applied  directly  to  the  rivet  pitches,  and  after  the  pitch  in  the 
end  panel  is  determined,  the  remaining  pitches  may  be  found  by  means 
of  a  slide  rule  without  the  corresponding  shears  being  found.  This  ap- 
proximate solution  for  uniformly  distributed  loads  gives  safe  results 
even  though  there  is  additional  dead  load,  but  enough  rivets  may  be 
saved  to  justify  computing  the  live  and  dead  load  shears  separately. 
Sometimes  this  approximate  method,  or  some  similar  method,  is  applied 
to  girders  which  support  moving  concentrated  loads,  -  but  this  is  not 
recommended.  The  shears  thus  found  are  less  than  the  shears  computed 
separately,  and  consequently  the  resulting  pitches  are  larger  than  they 
should  be.  This  difference  in  pitch  in  some  panels  of  deck  girders 
under  Cooper's  engine  loads  often  reaches  f".  In  view  of  this  it 
seems  best  to  compute  the  maximum  total  shears  for  each  panel  by 
means  of  the  diagram,  in  much  the  same  manner  as  in  the  problem  on 
page  251  : 1. 

1.  Illustrative  Problem  —  Moving  Uniform  Loads.  —  Find  the  rivet 
pitches  in  the  girder  designed  on  page  222  :  2,  using  a  unit  stress  in  bearing 
of  24,000#/sq.  in. 

9190#  =  r  =  value  of  one  £"  rivet  bearing  in  a  TV'  plate  (page  310) 
65.25"  =72J-  (2x2i+2f)  =  dr 
6000#/ft.  =  live  load 
560#/ft.  =  200  +  360  =  dead  load 

3040#  =  560  x  65.25  -f-  12  =  change   in   dead-load    shear    per    panel 
length  equal  to  dr 

11  =  60  X  12  ~  65.25  approximate  number  of  panels. 

The  live-load  shear  at  the  beginning  of  the  2nd  panel  will  then  be  [— ) 

of  the  live  load  end  shear.  This  is  simpler  than  using  actual  lengths  in 
the  proportion. 


Shear  V  (in  thousands) 

Panel 

p.    ,        9.19  X  65.25 

y      - 

Dead 

Live 

Total 

End 

17  =  .56  x  30 

180  =-  6.0  x30 

197 

3 

2nd 

14  =  17  -  3 

149  =  180  x  (|f)2 

163 

3i 

3rd 

11  =  14  -  3 

120  =  180  x  (T9T)2 

131 

4* 

4th 

8  =  11  -3 

95  =  180  x  (T8T)2 

103 

5i 

5th 

6    max. 

The  use  of  the  approximate  method  illustrated  below  would  give  the 
same  results  in  this  case  because  the  total  dead  load  is  so  small  compared 
to  the  live  load. 


3.04 


9190  x  65.25 


6560  x  30 
3f  =  3.04  x  (H)2  = 

4J  =  3.04x(-V-)2  = 
5|  =  3.04  x  (-V-)2  = 


pitch  in  end  panel 

• 

"      "    2nd     " 

"      "    3rd     " 

«      «   4th     « 


CASE   V  — LOADS   APPLIED   TO   THE   FLANGE 

2.  How  Applied.  —  One  or  more  stiffening  angles  should  be  placed 
under  each  heavy  concentrated  load  which  rests  on  the  top  flange  of 
a  girder,  in  order  to  transmit  the  load  to  the  web  plate.  The  rivet  pitch 
is  then  found  according  to  the  method  of  Case  III.  Obviously,  stiffening 
angles  cannot  be  used  under  moving  concentrated  loads  or  under  eithei 
static  or  moving  uniformly  distributed  loads.  The  only  way  in  which 
these  flange  loads  may  be  transmitted  to  the  web  plate  is  by  means  01 
the  flange  rivets.  These  rivets,  therefore,  must  resist  not  only  the  sam< 
horizontal  flange  stresses  which  they  would  resist  in  case  the  same  load: 
were  .applied  directly  to  the  web,  but  they  must  resist  also  a  vertica 
stress.  This  form  of  loading  is  very  common.  For  example,  the  rail 
of  crane  runways  rest  directly  upon  the  tops  of  the  crane  runway  girders 
and  the  tracks  of  railway  bridges  rest  directly  upon  the  tops  of  th 
stringers  of  through  bridges  and  the  tops  of  the  girders  of  deck  bridges 


CHAPTER   XXXVII 


RIVETS  IN  THE  FLANGES  OF  PLATE   GIRDERS 


249 


Similarly,  masonry  walls  are  often  built  upon  the  tops  of  girders.  The 
ties  of  railroad  tracks  are  so  close  together  that  they  may  be  considered 
as  uniformly  distributed  loads.  In  order  that  this  vertical  stress  may  be 
properly  distributed  among  the  rivets,  the  pitch  should  not  exceed  4  or 
^  inches;  4  inches  is  used  for  crane  runway  girders,  and  4J  for  other 
deck  loads. 

1.  Theory.  —  In  order  to  combine  the  effects  of  both  horizontal  and 
vertical  stresses  on  the  rivets,  they  must  be  reduced  to  a  common  basis. 
For  convenience,  both  the  horizontal  and  the  vertical  components  are 
found  in  pounds  per  linear  inch  of  girder,  measured  horizontally.  The 
resultant  stress  shows  the  maximum  stress  per  linear  inch  to  be  resisted 
by  the  flange  rivets.  The  rivet  pitch  in  any  panel  is  found  by  dividing 
the  value  of  one  rivet  by  the  proper  resultant  stress,  thus: 


P  = 


resultant ' 


The  horizontal  component  per  linear  inch  was  found  by  the  shear  theory 

V 
on  page  244  : 1  to  be  -r.     It  could  be  found  by  the  bending  moment 

VB 

theory  on  page  243  : 3  by  dividing  the  stress  per  panel  -yr—  by  the  length 

VB  V        V 

of  the  panel  in  inches,  thus :    -yr—  -=-  12B  =  77-^  =  -j-.     The    V  and  the 


dr  are  found  in  exactly  the  same  way  as  if  the  loads  were  applied  to  the 
web,  the  shear  being  the  only  variable.  The  vertical  component  is  usually 
constant  throughout  the  full  length  of  the  girder.  It  may  be  composed 
of  several  parts,  including  the  proper  proportion  of  all  loads  which  stress 
the  rivets  vertically,  such  as  the  maximum  wheel  load  with  impact  or  the 
maximum  uniform  live  load,  the  dead  load  due  to  the  track  or  other 
superimposed  loads,*  and  the  weight  of  the  angles  and  cover  plates  of 
the  top  flange  of  the  girder  itself.  Most  of  these  loads  are  expressed  in 

*  Students  should  be  cautioned  against  two  common  mistakes.  The  weight  of 
track,  including  ties,  service  rails,  steel  and  wooden  guard  rails  and  fastenings,  is 
usually  given  in  pounds  per  linear  foot  of  track,  and  should  be  divided  by  2  to  give 
the  weight  per  foot  of  girder.  The  weight  of  rails  is  given  in  pounds  per  yard  and 
act  pounds  per  foot. 


pounds  per  linear  foot,  from  which  the  vertical  component  per  linear 
inch  may  be  found  by  dividing  by  12.  It  would  be  impossible  to  transmit 
the  whole  of  a  heavy  wheel  load  to  the  web  through  the  single  rivet 
directly  under  the  point  of  contact  of  the  wheel.  This  is  unnecessary 
because  the  rail  and  the  top-chord  angles  acting  as  beams  distribute  the 
load  among  several  rivets.  It  is  customary  to  consider  the  load  of  a 
crane  wheel  to  be  distributed  over  30  inches.  In  railway  bridges  it  is 
commonly  specified  that  the  maximum  wheel  load  is  distributed  over 
three  ties.  This  amounts  to  about  36  inches,  as  for  example,  when  8-inch 
ties  are  separated  by  6-inch  spaces.  The  maximum  wheel  load  of  Cooper's 
loading  is  one  of  the  heavy  drivers  except  for  short  spans  in  which  the 
maximum  shears  are  obtained  from  the  two  special  loads,  in  which  case 
one  of  the  special  loads  is  used.  The  impact  should  be  included;  when 
this  depends  upon  the  loaded  length  of  the  track  it  is  close  enough  to 
use  the  span  length.  The  resultant  stress  per  linear  inch  may  best  be 
determined  graphically,  either  by  means  of  'the  diagram  on  page  312  or 
by  the  use  of  a  simple  graph  constructed  for  each  problem  as  follows: 
lay  off  two  lines  at  right  angles  to  each  other,  or  use  two  edges  of  a 
rectangular  sheet  of  paper;  along  one  line  lay  off  the  constant  vertical 
component;  along  the  other  line  lay  off  the  different  horizontal  com- 
ponents; the  resultants  may  be  scaled  without  drawing  the  correspond- 
ing diagonal  lines. 

2.  Loads  are  sometimes  applied  to  the  bottom  flange.       If  the  loads 
are  divided  between  the  two  flange  angles  the  problem  is  the.  same  as 
for  loads  applied  to  the  top  flange.    If,  however,  the  loads  are  supported 
by  one  angle  only,  the  vertical  component  tends  to  shear  the  rivets  in 
single  shear,  while  the  horizontal  component  tends  to  shear  them  in 
double  shear,  although  the  bearing  value  in  the  web  usually  determines 
the  limiting  value.    Obviously  the  resultant  stress  cannot  be  found  from 
these  two  components  as  before.     Perhaps  the  simplest  treatment  is  to 
increase  the  vertical  component  by  the  ratio  which  the  bearing  value  of 
a  rivet  bears  to  the  single  shear  value,  and  then  proceed  as  before,  using 
the  bearing  value  for  r. 

3.  Illustrative  Problem  —  Uniform  Flange  Loads.  —  The  problem  on 
page  248  : 1  would  be  modified  as  follows,  if  the  load  were  applied  to  the 
top  flange  instead  of  the  web. 


250 


PART  III  — THE  DESIGN  OF  DETAILS 


6000#/ft.  =  live  load 
200#/ft.  =  superimposed  dead  load 

130#/ft.  =  (360  -  107)  -=-  2  =  weight  of  top  angles  and  cover  plates 
6330#/ft.  =  total  load  per  foot  supported  by  the  rivets 
530#/in.  =  6330  -=-  12  vertical  component  per  linear  inch. 

y 

The  values  of  j  are  found  from  the  total  shears  given  on  page  248  :  1. 


Panel 

V 
65.25 

Pitch         919° 

Resultant  =  \/(g^-5)!+  530. 

resultant 

End 

3020 

3070 

3 

2nd 

2500 

2560 

31 

3rd 

2010 

2080 

4* 

4th 

4J  max. 

1.  Illustrative  Problem  —  Concentrated  Flange  Loads.  —  See  page  251  : 1. 

CASE  VI— GIRDERS   IN  WHICH  THE  WEB   IS   CONSIDERED   TO   RESIST 
PART   OF   THE   STRESS   DUE   TO   BENDING    MOMENT 

2.  Method.  —  Probably  the  large  majority  of  girders   are  designed 
according  to  the  method  of  Case  B  (page  223 : 3)  in  which  the  resisting 
moment  of  the  web  plate  is  considered.     In  all  these  girders  the  rivet 
pitches  should  be  determined  accordingly.     In  this  method  of  design  a 
portion  of  the  web  plate  (usually  |  of  the  gross  area)  is  combined  with  the 
net  area  of  the  flange  angles  and  cover  plates  to  form  the  flange  area 
which  resists  the  flange  stress  due  to  bending  moment.     That  part  of 
the  flange  stress  which  is  resisted  by  the  web  plate  requires  no  rivets. 
This  is  analogous  to  a  simple  rectangular  beam.     The  flange  rivets  are 
required  to  transmit  the  remaining  stress  to  the  angles  and  the  cover 
plates,  and  to  provide  for  any  vertical  stress  which  may  result  from  loads 
applied  to  the  flange.    Thus  the  methods  of  the  preceding  cases  may  all 
be  modified  to  apply  to  girders  which  are  designed  by  the  method  of 
Case  B  by  substituting  for  V  a  new  value  V.    This  affects  the  horizontal 
component  of  the  stress  in  the  rivets,  but  it  does  not  affect  the  vertical 
component  which  remains  the  same  as  before.    The  new  value  V  bears 


the  relation  to  V  that  the  net  area  of  the  flange  and  cover  plates  bears 
to  the  total  flange  area  including  one-eighth  or  other  portion  of  the  web 
plate.  Thus  in  finding  the  pitch  in  any  panel, 


V  = 


in  which  V  is  the  maximum  shear  used  in  finding  the  pitch  according  to 
the  method  of  one  of  the  preceding  cases,  V  is  the  corresponding  value 
used  in  the  method  of  this  Case  VI,  a'  is  the  greatest  net  area  of  the 
flange  angles  and  cover  plates  of  one  flange  in  the  given  panel,  and  a  is 
the  sum  of  a'  and  the  part  of  the  web  plate  considered  as  flange  area, 

usually  I  of  the  gross  area.    The  ratio  —  is  not  constant  in  a  girder  unless 

the  same  flange  area  is  maintained  throughout  its  length.  When  cover 
plates  are  used,  the  maximum  section  is  furnished  near  the  point  of  maxi- 
mum flange  stress,  but  it  is  customary  to  cut  off  each  cover  plate  at  a 
point  where  the  reduced  area  is  sufficient  to  carry  the  maximum  flange 
stress  which  can  occur  at  that  point,  as  explained  in  the  next  chapter 
(page  259).  Hence  the  lengths  of  the  cover  plates  should  be  determined 

before  the  rivet  pitches  are  computed.    Since  the  ratio  —  increases  with 

the  area,  the  greatest  cross  section  in  any  panel  should  be  used;  this 
will  be  found  at  the  end  of  the  panel  nearer  the  center  of  the  girder.  If 
it  is  not  feasible  to  determine  the  lengths  of  the  cover  plates  before  the 
rivet  pitches  are  found,  the  maximum  ratio  found  from  the  greatest 
flange  area  should  be  used  throughout  the  whole  girder. 

It  is  usually  better  to  maintain  the  same  pitch  throughout  a  panel  rather  than 
to  change  it  at  the  end  of  a  cover  plate  because  such  a  change  would  result  in  the 
use  of  a  few  spaces  at  a  pitch  smaller  than  the  pitch  either  to  the  right  or  to  the  left. 
This  should  be  avoided  for  the  sake  of  appearance,  particularly  as  long  as  very  few 
rivets,  if  any,  would  be  saved.  If  this  greatest  section  extends  for  only  a  very  small 
proportion  of  the  panel  length,  the  smaller  area  may  be  used,  except  for  fixed  con- 
centrated loads,  because  the  shear  at  that  end  of  the  panel  is  less  than  at  the  be- 
ginning of  the  panel. 

3.  Illustrative  Problem  —  Web  Loads.  —  Find  the  rivet  pitches  in 
the  girder  designed  on  page  225 : 1.  The  concentrated  loads  found  on 


CHAPTER   XXXVII 


RIVETS   IN  THE  FLANGES  OF  PLATE  GIRDERS 


251 


page  225 :  1  are  placed  according  to  Fig.  251  (a)  to  give  the  maximum 
bending  moment.  This  position  also  gives  the  maximum  shear  in  the 
second  panel  =  84.2  thousand  pounds  =  164.3  -  80.1.  The  maxi- 
mum shear  in  the  end  panel  is  194.7  thousand  pounds,  obtained  when 


so.i      isr.2     102.4 

15        \      IS       I      /5       I      15 
184,3 


I75.4\ 


157.2       102.4       102.1 
IS        |      IS       j      IS       I       15 


\I94.7 


Fig.  251  (a). 


Fig.  251  (6). 


the  loads  are  placed  to  give  the  maximum  bending  moment  at  the  end 
of  the  first  panel,  which  brings  the  maximum  concentration  at  the 
quarter  point,  as  shown  in  Fig.  251  (6). 

9190#  =  r  =  value  of  one  f"  rivet  bearing  in  a  Ty  plate  at  24,000#/sq.  in. 
65.25"  =  72J  -  (2  x  2J  +  21)  =  dr 
12,300#  =  410  x  30  =  end  shear  due  to  weight  of  girder 
6,200#  =  12,300  -  410  X  15  corresponding  shear  for  second  panel 
37.1  13.9  +  8.2  +  7.5+7.5  .    a', 

4TT  =  3. 9  +  13.9  +  8.2+7. 5  +  7. 5  '  ratl°  o  f°r  2nd  panel 


29.6      37.1-7.5 


=  ratio  for  end  panel,  see  Fig.  262 


33.5      41.1-7.5 

OQ   ft 

182.9  =  ^~  (194.7  +  12.3)  =  V  for  end  panel  in  thousand  pounds 


81.6  = 

31"  = 

6"  max  = 


33.5 
37.1 
41.1 
9.19  X65.25 

182.9 
9.19  X65.25 


(84.2  +  6.2)      =  V   "   2nd 
=  pitch  in  end  panel 
=    "      "  2nd     ' 


81.6 


1.  Illustrative  Problem  —  Flange  Loads.  —  Find  the  rivet  pitches 
in  a  stringer  for  the  same  bridge  as  the  preceding  problem.  The 
stringer  is  composed  of  a  22  x  f  web  and  6  x  6  x  \^  angles  without 
cover  plates. 

3,130#  =  value  of  one  \"  rivet  bearing  in  a  f"  plate  at  24,000#/sq.  in. 


15"  =  221  -  (2  X  2J  +  21)  =  dr  (the  web  being  flush  with  top  angles) 
The  panel  length  is  taken  equal  to  dr.  The  dead-load  end  shear  is  2800# 
=  (±si  +  150)  7.5,  which  is  reduced  by  500#  =  375  X  1.25  per  panel. 
The  live-load  shears  for  the  first  two  panels  are  found  by  means  of  the 
table  on  page  318.  The  remaining  live-load  shears  are  maximum  for 
the  two  special  37,500#  loads  spaced  7  feet  apart,  since  the  loaded  segment 
does  not  exceed  12.5  feet  (page  194:1).  A  single  impact  percentage 
determined  from  the  span  length  may  be  used  for  each  panel.  The  con- 


stant  ratio  — 
a 


14.2 
15.9 


14.2 


The  vertical  component  per  linear 
30,000  : 


1.7  +  14.2 

inch  for  the  two  end  panels  is  1650# 
being  the  weight  of  the  top  flange  angles.    The  vertical  component  for 
the  remaining  panels  is  2050#  =  37'5QQ  x  *tf  + 

OD 


Panel 

V 

Horizontal  Component  =  — 
13 

Vertical 
Component 

Resultant 

Pitch         13'13° 

resultant 

End 

7140  =  (60,000  X^+  2800)^-5-15 
\               315             /  15.  9 

1650 

7330 

il 

/               615             \14.2 

2nd 

1650 

6450 

2 

\               315             /15.9 

3rd 

5330  =  (45,000  x^+  180o)^+15 
\            oio          /  lo.  y 

2050 

5710 

2t 

/              615             \14  2 

4th 

4^80    l^ssmv       i  i^nnl         •  T? 

2050 

5020 

2i 

rrOow  =  1  oo.oiJU  )\           -p    lov/U  1              -r  J.O 

\              315             /15.9 

5th 

3820  =  (32,500x|f+    800)||,15 

2050 

4340 

3 

/              615             \14.2 

fifV> 

*in°n    [  '~*P  '*oo  ~  *       i    "'on  1         ~  1  ^ 

on^n 

O7nn 

Din 

A     :          315         '     /15.9  ' 

^uou 

O/IA/ 

1 

The  rivet  pitches  are  here  determined  up  to  the  center  in  order  to 
illustrate  the  method,  although  as  a  matter  of  fact  they  could  not  be 
used  because  the  pitch  in  the  end  panel  is  less  than  the  minimum  of  2| 
found  from  the  table  on  page  306.  In  this  case  the  girder  should  be 
redesigned  with  either  an  increased  web  thickness  or  increased  depth. 


252 


PART   III  — THE   DESIGN   OF  DETAILS 


CASE    VH— BOX    GIRDERS,    CANTILEVER    GIRDERS,    AND    GIRDERS 
WITH    NON-PARALLEL    FLANGES 

1.  A  box  girder  may  be  considered  as  two  or  more  girders,  depending 
upon  the  number  of  webs  (Fig.  95  (gr)).    The  cross  section  is  usually  made 
symmetrical  about  a  vertical  axis.    When  there  are  only  two  webs  each 
half  of  the  girder  will  carry  one-half  the  load,  and  one-half  the  total 
flange  stress  will  be  resisted  by  the  angle  (or  angles)  on  each  web  together 
with  one-half  the  cover  plate.     The  flange  rivets  in  each  web  must  be 
proportioned  for  this  half  stress,  according  to  the  method  of  one  of  the 
preceding  cases.    If  flange  angles  are  used  on  only  one  side  of  each  web, 
the  rivets  will  be  in  single  shear,  and  the  corresponding  rivet  value  must 
be  chosen.     Girders  with  three  webs  are  usually  designed  so  that  the 
center  portion  carries  one-half  the  total  load.    Thus  there  are  two  angles 
in  each  flange  on  the  central  web,  but  only  one  on  each  outer  web.    The 
central  web  should  be  thick  enough  to  make  the  value  of  one  rivet  twice 
the  single-shear  value  so  that  the  rivet  pitches  in  all  three  webs  will  be 
the  same.     Otherwise,  the  pitches  must  be  determined  separately. 

2.  In  a  cantilever  girder  the  rivet  pitches  may  be  determined  by  the 
method  of  one  of  the  preceding  cases  given  for  simple  girders,  but  care 
must  be  taken  that  the  proper  shear  is  used.    In  determining  the  pitch 
in  any  panel,  the  maximum  shear  in  the  panel  should  be  used.    Sometimes 
this  maximum  will  occur  when  the  section  is  taken  at  the  left  end  of 
the  panel  and  sometimes  when  it  is  taken  at  the  right  end,  depending 
on  the  position  of  the  panel  in  the  girder.    See  page  190  : 1  for  the  position 
of  moving  loads  which  will  cause  the  maximum  shears. 

3.  Illustrative  Problem  —  Cantilever  Girder.  —  Find  the  pitches  of  f " 
rivets  in  a  40-ft.  cantilever  girder  which  projects  10  ft.  beyond  one  of 
two  supports  which  are  30  ft.  apart.    The  total  static  load  is  4,000#/ft. 
including  the  weight  of  the  girder.    The  girder  is  composed  of  a  36  x  f 
web  and  6x4  angles.     The  unit  stress  in  bearing  is  20,000#/sq.  in. 
Assume  the  simplest  case  in  which  the  load  is  applied  to  the  web,  and  the 
resisting  moment  of  the  web  is  neglected. 

The  shear  and  moment  diagrams  for  this  form  of  loading  are  shown  in 
Fig.  193.  The  maximum  bending  moment  occurs  at  the  section  for 
which  the  shear  is  zero,  and  the  point  of  contraflexure  is  at  the  point 


where  the  bending  moment  is  zero.  The  bending  moment  and  shear, 
and  hence  the  rivet  spacing,  are  symmetrical  between  the  point  of  con- 
traflexure and  the  supported  end.  The  distance  from  the  right  support 
to  the  point  of  contraflexure  is  26 . 6  found  by  equating  to  zero  an  expres- 
sion for  bending  moment  in  terms  of  the  distance  X.  The  point  of  contra- 
flexure is  not  much  over  a  panel  length  from  the  left-hand  support  so 
the  equal  panels  are  laid  off  from  the  point  of  contraflexure  and  from  the 
right-hand  support  as  shown  in  Fig.  252  in  order  to  make  the  rivet  spacing 
symmetrical.  If  preferred, 

the  equal    panels    could    be    o    t  _2    3    4    _s    e    7    s  __  s    ?    e    s 

laid  off  from  the  left-hand 
support,  but  additional 
pitches  would  have  to  be  cal- 


^P1- 

Till                                  1        1        1        1 

LO&.7 


53,3 


Fig.  252. 


culated  because  the  shears  for  the  panels  at  the  right  would  differ  from 
those  at  the  left.    The  cantilever  end  is  divided  into  four  equal  panels. 


5630#  =  r 
31.5"  = 


value  of  one  f  "  rivet  bearing  in  a  f  "  plate 
-2x2j  =  dr. 


Panel 

Shear  =  V 
(in  thousands) 

Pit..,        5.63X31.5 

0-1 

10.0  =4.0  x2.5 

6  max. 

1-2 

20.0  =10.0  x2 

6  max. 

2-3 

30.0  =10.0  x3 

6 

3-4 

40.0  =10.0  x4 

4* 

4-5 

66.7  =  106.7  -40.0 

2| 

5-6 

53.3  =RR 

3i 

6-7 

42.9  =53.3  -4.0  x2.6 

H 

7-8 

32.5  =42.9  -4.0  x2.6 

5k 

8-8 

22.1  =32.5  -4.0  x2.6 

6  max. 

The  smallest  space  2f  is  not  less  than  the  minimum  2T7F  found  in  the 
bottom  table  on  page  306  so  the  solution  is  satisfactory. 

4.  Girders  with  non-parallel  flanges  are  used  for  turntables,  sidewalk 
brackets,  and  other  special  work.  The  inclined  flanges  have  vertical 
components  which  relieve  the  web  plate  of  part  of  the  shearing  stresses, 
and  the  number  of  rivets  must  be  increased  accordingly.  The  formula 


CHAPTER   XXXVII 


RIVETS   IN   THE   FLANGES  OF  PLATE   GIRDERS 


253 


p  =  T— •  ,  or  a  modification  of  it  for  conditions  similar  to  those  of  the  pre- 
ceding cases,  may  be  adapted  to  girders  with  inclined  flanges  by  substi- 
tuting V"  for  V,  as  explained  below.  The  resulting  pitch  will  be  the 
distance  along  the  flange  and  not  necessarily  horizontal.  The  pitch  along 
the  bottom  flange  will  theoretically  be  the  same  as  the  pitch  along  the 
top  flange  even  though  the  inclination  is  not  the  same.  Sometimes  for 
practical  reasons,  only  the  pitch  of  the  rivets  in  the  steeper  flange  is  com- 
puted, the  rivets  in  the  other  flange  being  placed  in  the  same  vertical 
lines  even  though  more  rivets  are  thus  used.  The  pitch  is  usually  changed 
at  equal  intervals.  Since  both  V"  and  dr  vary,  the  pitches  should  be 
determined  at  both  ends  of  a  panel  and  the  smaller  of  the  two  should  be 
used  throughout  that  panel.  The  value  of  V"  may  be  determined  from 
the  following  expression :  * 

V"  =  F-^(tana+tan/3) 

Clr 

in  which  V  =  the  maximum  shear  for  a  given  section,  M  =  the  cor- 
responding bending  moment  for  the  same  section  and  for  the  same  posi- 
tion of  the  loads,  dr  =  the  vertical  distance  between  rivet  lines  at  the 
given  section,  a  and  /8  =  the  angles  of  inclination  of  the  bottom  and  the 
top  flanges  with  the  horizontal.  The  signs  of  the  tangents  given  above 
are  based  upon  the  flanges  converging  toward  the  end  of  the  girder. 
In  case  either  slope  is  reversed  the  corresponding  sign  of  the  tangent 
should  be  changed.  If  either  flange  is  horizontal  the  corresponding  tangent 
becomes  zero. 

CASE    vm— GIRDERS    WITH    VERTICAL   FLANGE    PLATES,    AND 
GIRDERS    WITH    FOUR    ANGLES    IN    EACH    FLANGE 

1.  When  Used.  —  Girders  which  carry  heavy  loads  over  long  spans 
frequently  require  greater  flange  areas  than  can  be  furnished  by  two 
angles  with  cover  plates.  Similarly  the  use  of  a  depth  less  than  the  most 
economical  depth  may  necessitate  the  use  of  a  more  complex  flange. 

*  For  derivation  see  Johnson-Bryan-Turneaure's  "Modern  Framed  Structures," 
Vol.  Ill,  John  Wiley  and  Sons,  Inc.,  New  York;  or  Waddell's  "Bridge  Engineering," 
Vol.  I,  John  Wiley  and  Sons,  Inc.,  New  York. 


Various  forms  of  flange  are  adopted  to  meet  different  requirements,  as 
illustrated  in  books  on  girder  design.  Only  two  forms  will  be  considered 
here,  viz.:  flanges  with  vertical  plates  between  the  angles  and  the  web, 
and  flanges  composed  of  four  angles.  Vertical  flange  plates  are  often 
used  in  conjunction  with  the  four  angles,  either  between  the  angles  and 
the  web  or  outside  of  the  vertical  legs  of  the  angles,  or  both,  but  any 
draftsman  who  is  likely  to  design  the  details  for  such  a  girder  should  be 
able  to  adapt  the  principles  of  this  chapter  to  his  needs. 

2.  Vertical  flange  plates  which  are  placed  between  the  flange  angles 
and  the  web  plate  extend  the  entire  length  of  the  girder  because  it  is 
impractical  to  make  them 
shorter  than  the  angles  which 
rest  upon  them.  The  rivets 
which  pass  through  both  the 
angles  and  the  vertical  plates 
(rows  a  and  b,  Fig.  253)  must 
be  considered  separately  from 
those  which  pass  through  the 
web  and  the  vertical  plates 
only  (row  c).  The  former  pig.  253. 

transmit  only  that  portion  of 

the  flange  stress  which  is  carried  by  the  flange  angles  and  the  cover 
plates.  This  part  of  the  stress  tends  to  shear  the  rivets  between  the 
angles  and  the  vertical  plates,  and  the  thickness  of  metal  is  sufficient 
to  develop  the  full  double-shear  value  of  the  rivets.  The  total  stress 
carried  by  the  angles,  the  cover  plates,  and  the  vertical  flange  plates 
tends  to  shear  the  rivets  in  all  rows  between  the  vertical  plates  and 
the  web,  and  the  rivet  value  is  usually  limited  by  the  bearing  value  in 
the  web  plate.  For  practical  reasons  it  is  customary  to  place  the 
rivets  in  row  c  opposite  those  hi  rows  a  and  b.  The  pitch  in  row  c 
increases  more  rapidly  than  the  pitch  in  rows  a  and  b.  If  the  pitch  in 
rows  a  and  6  is  found  to  be  less  than  that  in  row  c  in  the  end  panel  it 
will  also  be  less  in  the  other  panels,  so  it  is  unnecessary  to  determine 
the  pitch  in  row  c  in  every  panel.  Sometimes  the  pitch  in  row  c  will 
be  twice  as  great  as  in  rows  a  and  6  in  some  panels,  and  the  rivets  may 
be  placed  opposite  those  in  row  a  only,  as  in  Fig.  253,  provided  the 


254 


PART  III  — THE   DESIGN   OF  DETAILS 


maximum  value  (usually  6")  is  not  exceeded.  The  pitch  in  row  c  must 
then  be  determined  in  enough  panels  to  find  where  the  double  pitch  may 
begin. 

1.  Theory  —  Rivets  in   Angles.  —  The   rivet   pitch   in   rows  a  and   b 

r"d 
is  determined  from  the  expression  p  =  -^—-, ,   in   which    r"  =  the   double 

shear  value  of  one  rivet,  dr  =  the  mean  depth  between  the  rivet  lines  in 
the  angles  (rows  a  and  b),  and  V"  =  that  proportion  of  the  maximum 
total  shear  V  in  the  panel  which  the  net  area  of  the  angles  and  the  cover 
plates  bears  to  the  total  net  flange  area  in  the  panel,  including  the  ver- 
tical flange  plates.  Since  this  proportion  increases  with  the  areas,  both 
areas  should  be  taken  for  a  section  at  the  end  of  the  panel  toward  the 
center  of  the  girder,  although  the  maximum  shear  is  not  found  for  the 
same  section  (compare  page  244  : 3).  The  resulting  pitch  is  the  horizontal 
distance  from  a  rivet  on  row  a  to  a  rivet  on  row  6,  the  rivets  being  stag- 
gered. If  three  rows  are  used  in  each  angle,  the  rivets  in  the  middle  row 
are  usually  staggered  with  the  rivets  in  the  top  and  bottom  rows  which 
are  placed  opposite.  The  pitch  from  a  rivet  in  the  middle  row  to  the  rivets 
in  the  other  rows  would  be  three-halves  of  the  pitch  found  from  the 
formula,  dr  being  the  mean  depth  of  the  three  rows.  If  the  loads  are 
applied  to  the  flange  of  the  girder,  a  vertical  component  must  be  com- 
bined with  the  horizontal  component  as  in  the  method  of  Case  V  (page 
248  :  2).  If  the  girder  is  designed  according  to  Case  B  (page  223  :  3),  the 
total  net  flange  area  mentioned  above  should  include  one-eighth  or  other 
portion  of  the  web  which  is  counted  as  flange  area,  as  explained  under 
Case  VI  (page  250  :  2). 

2.  Theory  —  Rivets  in    Vertical  Plates.  —  The    determination    of    the 
pitch  of  the  rivets  in  row  c  (Fig.  253)  is  based  upon  the  difference  between 
the  total  number  of  rivets  required  in  rows  a,  b,  and  c,  and  the  number 
required  in  rows  a  and  b.    The  total  number  of  rivets  in  all  three,  rows 

VB 
required  in  a  panel  of  B  feet  is  —^  (compare  page  243  : 3),  in  which  V 

=  the  maximum  total  shear  in  the  panel,  r  =  the  value  of  one  rivet  in 
bearing  in  the  web  (or  double  shear  if  less),  and  a"  =  the  mean  depth  of 

the  three  rows  of  rivets  or  -  — .    The  corresponding  number  of 

Q 


rivets  in  rows  a  and  b  is 


V'"B 

r"dr 


(preceding  paragraph).    The  number  of 


rivets  in  row  c  is  equal  to  the  difference  between  these  two  numbers,  and 
the  rivet  pitch  is  found  by  dividing  the  panel  length  by  this  difference. 
The  panel  length  cancels  out  and  the  formula  for  the  rivet  pitch  in  row  c  is 


p  = 


1 


V" 


rd'      r"dr 

If  the  loads  are  applied  to  the  flange  of  the  girder,  the  same  vertical 
component  used  in  finding  the  pitch  in  rows  a  and  b  should  be  combined 

and  also  with  —j-  to  give  two  resultants  which  should  be  used 


V 

with  -r. 
d 


in  place  of  the  corresponding  quantities  in  the  above  formula.  If  the 
girder  is  designed  according  to  Case  B,  the  V  of  the  formula  should  be 
replaced  by  V  as  in  Case  VI  (page  250  : 2)  and  the  V"  should  be  modi- 
fied as  in  the  preceding  paragraph.  In  case  a  deeper  vertical  plate  is 
used  with  an  additional  row  of  rivets,  the  rivets  would  be  staggered  on 
the  two  lines,  and  the  pitch  of  the  staggered  rivets  would  be  found  as 
before  except  the  extra  rivet  line  would  have  to  be  considered  in  deter- 
mining the  mean  depth  d'. 

3.  Illustrative  Problem  —  Girder  with  Vertical  Flange  Plates.  —  The 
points  peculiar  to  this  type  of  girder  may  be  illustrated  by  finding  the 
pitch  in  one  panel  where  the  maximum  shear  =  600,000#.  The  girder 
is  composed  of  a  120  X  f  web,  6x6  angles,  14"  cover  plates,  and  12  x  f " 
vertical  flange  plates,  with  J"  rivets.  Let  us  assume  that  the  resisting 
moment  of  the  web  is  considered;  that  the  ratio  of  the  net  area  of  the 
angles,  cover  plates,  and  vertical  plates  to  the  total  net  area  including 
I  the  web  is  0.8,  or  V  =  0.8F;  and  that  the  ratio  of  the  net  area  of  the 
angles  and  cover  plates  to  this  same  total  net  area  is  0 . 6,  or  V"  =  0 . 6  V. 
The  depth  back  to  back  of  angles  is  10'  OJ",  the  distance  from  the  back 
of  the  angle  to  the  first  row  of  rivets  a  is  1\,  from  row  a  to  row  6  is  2}, 
from  row  b  to  row  c  is  3,  and  from  row  c  to  row  d  (the  additional  row  in 
the  vertical  plates)  is  3.  The  mean  depth  dr  of  the  rows  a  and  b  is  113}, 
and  the  mean  depth  d'  of  rows  a,  b,  c,  and  d  is  107 . 6.  From  the  last  table 
on  page  310,  the  value  of  one  rivet  in  double  shear  r"  =  12,030,  and 


CHAPTER   XXXVII 


RIVETS   IN   THE   FLANGES   OF   PLATE   GIRDERS 


255 


in  bearing  in  the  f "  web  plate  r  =  10,940.    The  pitch  of  the  staggered 

,,      12,030  x  113.25     _, 

rivets  in  rows  a  and  o  is  3j  =  -^ .     Ihe  pitch  of  the  stag- 

0.6  X  6UU,OOU 

gered  rivets  in  rows  c  and  d  is  calculated  to  be  over  the  maximum  of  six 
inches,  thus: 

1 

0.8  X  600,000  0.6  x  600,000 


10,940  x  107.6        12,030  x  113.25 

Since  6"  is  less  than  2  x  3f  the  double  space  cannot  be  used,  and  for 
practical  reasons  a  pitch  of  3f  would  be  used,  with  the  rivets  in  rows  c 
and  d  opposite  those  in  rows  a  and  b.  In  case  the  load  was  applied  to 
the  flange  and  the  vertical  component  was  1000#  per  linear  inch  of  girder, 
the  above  problem  would  be  modified  as  follows.  The  horizontal  component 

— j—  =  3280  =  -  -   must  be  replaced   by  the  resultant  of  this 

dr  llo.^O 

force  and   the  vertical   component  of   1000,  or  3430.      The  horizontal 


component 


AAM 
=  4460  = 


x  600,000 
-- 
i(j  t  .o 


. 
must  be  replaced  by  the  resultant 


of  this  force  and  1000,  or  4750.    The  rivet  pitch  in  rows  o  and  6  would 

12  030 
' 


then  be 

1 


4570         3430 


and   the  pitch   in  rows    c  and  d  would    become 


which  is  over  6".    A  pitch  of  32  would  be  used  since  6" 


10,940      12,030 
is  less  than  2  x  3^. 

1.  When  four  angles  in  each  flange  are  used,  the  rivets  in  the  addi- 
tional angles  are  placed  opposite  those  in  the  outer  angles,  as  shown  in 
Fig.  255,  for  convenience  in  spacing  the  rivets  both  in  the  drafting  room  and 
in  the  shop.  It  is  therefore  necessary  only  to  determine  the  pitches  in 
either  the  outer  or  the  inner  angles  whichever  is  smaller.  The  rivets 
in  the  outer  angles  are  proportioned  for  the  entire  vertical  component 
due  to  any  load  which  rests  upon  these  angles,  and  for  that  portion  of 
the  horizontal  stress  which  is  carried  by  the  outer  angles  and  the  cover 
plates.  The  rivets  in  the  inner  angles  are  proportioned  simply  for  that 
part  of  the  horizontal  stress  which  is  carried  by  the  inner  angles  (unless 


there  should  be  a  vertical  load  applied  to  these  angles).    The  depth  dr 

should  be  the  mean  depth  between  the  rivet  lines  in  the  angles  in  which 

the  pitch  is  determined,  the 

mean  depth   for   the  inner 

angles    being    considerably 

less  than  that  for  the  outer 

angles.     When  cover  plates 

are  used,  the  limiting  pitch 

is  found  in  the  outer  angles, 

otherwise  the  pitches  in  both 

angles  should  be  determined 


in  one  or  more  panels  and 
the  smaller  values  chosen. 


Fig.  255. 


THE   DETERMINATION   OF   THE   MINIMUM   PITCH   BASED    UPON 
THE    STRENGTH    OF    THE   WEB 

2.  Importance.  —  One  point  of  failure  of  plate  girders  is  apparently 
overlooked  by  some  designers,  although  it  should  receive  the  most  care- 
ful consideration.  The  strength  of  the  web  plate  between  flange  rivets 
may  not  be  sufficient  to  transmit  the  full  flange  stress  for  which  the 
flanges  are  designed  and  for  which  the  rivet  pitches  are  determined.  If 
the  rivet  pitch  which  is  determined  by  any  of  the  methods  of  the  preced- 
ing. Cases  happens  to  be  less  than  a  certain  minimum,  the  web  plate  will 
fail  along  the  line  of  rivets  before  the  strength  of  the  rivets  is  fully  devel- 
oped, and  the  maximum  safe  load  of  the  girder  will  be  somewhat  less 
than  the  required  amount.  The  minimum  space  of  "  three  diameters  " 
(page  68 : 6  )  is  so  generally  recognized  as  the  smallest  pitch  allowed 
for  rivets  in  a  single  line  that  no  serious  difficulty  is  likely  to  arise  from 
the  lack  of  further  consideration  of  flange  rivets  which  are  placed  in  a 
single  line,  although  the  minimum  pitch  is  not  exactly  three  times  the 
diameter  of  the  rivet  for  all  unit  stresses.  A  draftsman  is  quite  liable, 
however,  to  use  a  smaller  pitch  for  staggered  rivets  than  is  justified  by 
the  strength  of  the  web  plate.  Although  the  minimum  pitch  for  stag- 
gered rivets  is  somewhat  less  than  "  three  diameters,"  it  is  not  so  much 
less  as  many  designers  and  draftsmen  suppose.  It  is  important  that  no 


256 


PART  III  — THE   DESIGN  OF  DETAILS 


pitch  be  less  than  the  minimum  determined  by  the  strength  of  the  web  as 
explained  below. 

1.  A  table  of  minimum  pitches  for  flange  rivets  is  given  on  page  306. 
Values  are  shown  for  different  sizes  of  rivets,  for  different  web  thicknesses, 
and  for  different  unit  stresses.     Distinction  is  made  also  between  rivets 
placed  in  single  and  double  rows,  and  between  those  which  act  in  single 
and  double  shear.    It  should  be  noted  that  the  pitch  varies  with  the  web 
thickness  only  when  the  rivet  value  is  limited  by  either  single  or  double 
shear,  but  the  pitch  is  independent  of  the  web  thickness  when  the  rivets 
are  limited  by  the  bearing  value  as  is  more  frequently  the  case.    Values 
are  given  in  the  tables  only  for  webs  from  -j^"  to  f "  thick,  and  no  value  is 
given  which  would  provide  less  than  the  minimum  clearance  required 
in  driving  the  rivets  by  machine.     Since  rivets  are  so  commonly  stag- 
gered on  lines  which  are  2j"  apart  it  has  seemed  desirable  to  indicate 
by  italics  all  values  which  are  less  than  the  minimum  determined  for  this 
gage  from  the  diagram  on  the  page  preceding  the  table.     These  values 
in  italics  should  be  used  only  upon  the  assurance  that  the  corresponding 
reduction  in  the  net  flange  area  will  not  impair  the  strength  of  the  girder. 
For  example,  this  is  true  when  rivets  in  both  lines  have  been  deducted 
in  determining  the  net  area  used  in  the  design  of  the  flange,  or  when  there 
is  sufficient  excess  of  flange  area  in  the  panel  for  which  the  pitch  is  de- 
termined as  is  quite  often  the  case. 

2.  Unit  Stresses.  —  The  unit  stress  in  shear  is  usually  specified  for 
the  gross  area  of  the  web  plate  but  seldom  for  the  net  area.     In  deter- 
mining the  strength  of  the  web  between  rivets  the  net  area  is  used.    In 
the  tables  two  different  unit  stresses  in  shear  on  the  net  section  of  the 
web  are  used  in  conjunction  with  the  common  unit  stresses  for  the  rivets. 
Unless  otherwise  specified  a  unit  stress  of  13,000#/sq.  in.  may  be  used. 
This  is  about  eight-tenths  of  the  unit  stress  in  tension  of  16,000,  which 


is  a  fair  allowance.  It  is  also  about  four-thirds  of  the  unit  stress  in  shear 
on  the  gross  section  of  10,000,  which  is  consistent  with  the  ratio  used  in 
allowing  for  rivets  in  the  web  plate  in  deriving  the  formula  used  for 
designing  girders  by  the  method  of  Case  B  (see  page  223: 3).  Incidentally, 
the  use  of  13,000  with  the  unit  stresses  for  rivets  as  specified  by  the 
American  Railway  Engineering  Association  remits  in  a  minimum  pitch 
in  a  single  row  of  rivets  of  three  diameters,  as  shown  in  the  first  table  on 
page  306. 

3.  Theory.  —  The  web  plate  must  be  strong  enough  to  transmit  the 
flange  stress  to  the  flange  angles.  The  critical  horizontal  section  is  along 
the  line  of  flange  rivets.  When  two  lines  of  rivets  are  used,  the  critical 
section  will  be  along  the  line  nearer  the  center  of  the  web.  The  web 
between  adjacent  rivets  on  the  critical  line  must  develop  the  strength 
of  the  corresponding  number  of  rivets,  i.e.,  one  when  a  single  line  is  used 
as  in  Fig.  257  (a)  and  two  when  the  rivets  are  staggered  as  in  Fig.  257  (6). 
The  formulas  upon  which  the  values  in  the  tables  on  page  306  are  based 
depend  upon  whether  rivet  values  are  limited  by  bearing,  or  by  single 
or  double  shear.  The  formulas  for  the  minimum  pitch  for  rivets  in  a 
single  line  and  for  staggered  rivets  are  so  similar  that  they  are  derived 
in  parallel  columns  for  the  sake  of  comparison.  Similar  expressions  for 
three  or  more  lines  of  rivets  may  be  derived  in  like  manner  as  occasion 
demands.  Let  p  =  the  minimum  rivet  pitch,  measured  parallel  to  the 
rivet  lines  from  center  to  center  of  rivets,  d  =  the  diameter  of  the  rivet, 
d  +  l  =  the  diameter  of  the  rivet  hole  used  in  designing  (page  208:2), 
t  =  the  thickness  of  the  web  plate  (or  the  thickness  of  a  single  angle  of 
a  box  girder  if  less  than  the  web  thickness),  s  =  the  unit  stress  in  shear 
on  the  net  section  of  the  web  plate,  s'  =  the  unit  stress  in  shear  on  the 
rivets,  and  b  =  the  unit  stress  in  bearing.  All  units  are  inches  or  pounds 
per  square  inch. 


CHAPTER  xxxvn  RIVETS   IN  THE  FLANGES  OF  PLATE  GIRDERS 

RIVETS   IN  SINGLE  LINE  STAGGERED  RIVETS 


257 


Fig.  257  (a). 
In  Fig.  257  (a),  the  net  area  which  resists  horizontal  shear  in  the  space 


Fig.  257  (6). 

In  Fig.  257  (6),  the  net  area  which  resists  horizontal  shear  in  the  space 
P  is  [p  -  (d  +  |)]<.    This  is  multiplied  by  the  unit  stress  s  and  equated  to     2p  is  [2p  -  (d  +  £)]<.    This  is  multiplied  by  the  unit  stress  s  and  equated 

to  the  value  of  two  rivets. 


the  value  of  one  rivet. 

//  the  rivets  are  limited  by  the  bearing  value: 


//  the  rivets  are  limited  by  the  bearing  value: 


or 


If  the  rivets  are  limited  by  the  single  shear  value: 


irdV 
or        P  =  -J7T  + 


N> 


If  the  rivets  are  limited  by  the  single  shear  value: 
2ircPs' 


or 


P  = 


If  the  rivets  are  limited  by  the  double  shear  value: 


or        p  = 


IT  d?s' 
2ts 


If  the  rivets  are  limited  by  the  double  shear  value: 

2  x  2T  dV 


or 


SUMMARY 


CASES  I,  n,  m,  and  IV.     Girders  in  Which  the  Loads  are  Applied 
to  the  Web  and  the  Resisting  Moment  of  the  Web  is  Neglected.  —  The 

rd 
maximum  pitch  in  each  panel  is  found  from  p  =  -^  in  which  r  =  the 

limiting  value  of  one  rivet,  dr  =  the  mean  depth  between  the  rivet  lines 
of  the  top  flange  and  those  of  the  bottom  flange,  and  V  =  the  maximum 
total  shear  at  the  beginning  of  the  panel.  No  pitch  should  be  more  than 
6"  or  less  than  the  minimum  found  from  the  table  on  page  306.  The 
panel  lengths  are  chosen  approximately  equal  to  the  depth  between  rivet 
lines,  although  this  may  be  varied  somewhat  to  conform  to  the  spacing 
of  the  stiffening  angles.  The  pitch  is  also  changed  at  the  point  of  ap- 
plication of  any  fixed  concentrated  load.  If  there  are  no  other  loads 
besides  the  fixed  concentrated  loads  except  the  weight  of  the  girder, 
the  pitch  is  changed  only  at  these,  points  of  concentration.  For  girders 


which  support  moving  uniformly  distributed  loads  the  intermediate 
pitches  may  be  found  from  the  pitch  in  the  end  panel  as  explained  on 
page  247  : 3. 

CASE  V.    Girders  in  Which  the  Loads  are  Applied  to  the  Flange  and 
the  Resisting  Moment  of  the  Web  is  Neglected.  —  The  maximum  pitch 

in  each  panel  is  found  from  p  =  -          -r,  in  which  the  resultant  is  found 

resultant 

from  horizontal  and  vertical  compjjtfents  in  pounds  per  linear  inch.    The 

y 

horizontal  component  is  -=-  found  from  the  same  values  and  at  the  same 

dr 

points  as  in  Cases  I-IV  above.  The  vertical  component  is  found  from  the 
loads  which  tend  to  shear  the  rivets  vertically,  as  explained  on  page 
249  : 1.  No  pitch  should  exceed  4j"  (usually  4"  for  crane  runway  girders), 
or  be  less  than  the  minimum  found  from  the  table  on  page  306. 


258 


PART  III  — THE   DESIGN   OF  DETAILS 


CASE  VI.  Girders  in  Which  the  Web  is  Considered  to  Resist  Part 
of  the  Flange  Stress  due  to  Bending  Moment.  —  The  methods  of  Cases 
I  to  V  inclusive  may  be  made  to  apply  to  girders  designed  by  the  method 
of  Case  B  (page  223 : 3)  by  simply  multiplying  each  value  of  V  by  the 

ratio  — ,  where  a'  is  the  greatest  net  area  of  the  flange  angles  and  cover 

0 


plates  in  a  given  panel  and  a  is  the  sum  of  a'  and  that  portion  of  the  web 
plate  considered  as  flange  area  (usually  £  of  the  gross  area). 

CASE  VII.  Box  Girders;  see  page  252:1.  Cantilever  Girders;  see 
page  252  :  2.  Girders  with  Non-parallel  Flanges;  see  page  252  :  4. 

CASE  VIII.  Girders  with  Vertical  Flange  Plates;  see  page  253 :  2. 
Girder  with  Four  Angles  in  Each  Flange;  see  page  255:  1. 


CHAPTER  XXXVIII 
COVER  PLATES 

SYNOPSIS:  The  methods  of  finding  the  lengths  of  the  cover  plates  of  plate  girders  to 
be  used  under  different  conditions,  and  the  determination  of  the  rivet  spacing  in  the 
cover  plates. 


1.  Use.  —  Cover  plates  are  often  riveted  to  the  flange  angles  of  plate 
girders  in  order  to  furnish  the  necessary  flange  area  when  the  angles  alone 
are  insufficient,  as  explained  on  page  219 : 1.    The  use  of  cover  plates  which 
do  not  extend  the  full  length  of  the  girder  permits  the  reduction  of  flange 
area  toward  the  ends  of  the  girders  to  correspond  to  the  reduction  in  the 
flange  stress  due  to  bending  moment. 

LENGTHS    OF    COVER    PLATES 

2.  Some  cover  plates  extend  the  full  length  of  the  girder  in  order  to 
furnish  protection  from  the  weather,  or  to  give  uniform  bearing.     On 
girders  which  are  exposed  to  the  elements,  one  cover  plate  of  the  top 
flange  is  made  to  extend  the  entire  length  to  prevent  the  collection  of 
water  in  the  pocket  formed  between  the  angles  above  the  edge  of  the  web 
plate  (page  95:3).    Some  specifications  require  that  one  of  the  bottom 
plates  extend  the  full  length  also,  particularly  in  bridges  over  salt  water. 
This  keeps  the  girder  symmetrical  about  the  neutral  plane,  although  no 
harm  can  come  from  having  an  excess  in  one  flange  even  though  it  is  not 
balanced  by  an  excess  in  the  other.    In  crane  runways  the  rails  usually 
rest  directly  upon  the  top  flanges  of  the  girders,  and  in  order  to  give 
proper  bearing  for  the  rails  all  the  top  cover  plates,  or  the  cover  channel 
(Fig.  95  (e)),  must  run  the  full  length.    This  is  not  required  in  the  top 
flanges  of  deck  railway  bridge  girders  because  the  ties  can  be  notched  to 
make  up  for  the  variation  in  the  thickness  of  the  plates. 


3.  The  theoretical  length  of  a  cover  plate  is  determined  from  the  curve 
of  bending  moments,  but  the  actual  length  is  usually  made  from  two 
to  three  feet  greater.    (Compare  pages  261 :  2  and  262:  2.)    This  extension 
of  one  foot  or  more  at  each  end  permits  the  partial  development  of  the 
plate  by  rivets  beyond  the  point  where  the  plate  theoretically  begins, 
thus  insuring  its  action  when  needed.     The  extension  also  provides  a 
safe  margin  for  any  inaccuracies  in  length  due  to  scaling  the  graph  or  to 
calculation,  and  minimizes  the  chance  of  the  girder  failing  at  the  end  of  a 
cover  plate. 

4.  The  graphic  method  of  determining  the  theoretical  lengths  of  cover 
plates  will  be  explained  first  because  it  is  more  general  in  that  it  can  be 
adapted  to  any  condition  of  loading.    The  algebraic  method  is  more  con- 
venient than  the  graphic  method  upon  which  it  is  based,  but  it  is  limited 
to  uniformly  distributed  or  moving  loads,  as  explained  on  page  263: 1. 

5.  For  girders  which  are  symmetrically  loaded  only  one-half  of  the 
span  need  be  plotted.    This  is  true  also  for  girders  with  unsymmetrical 
loads  which  may  be  reversed,  as  in  bridges.     For  unsymmetrical  fixed 
loads  the  full  length  should  be  plotted.     Usually  the  curve  of  bending 
moments  for  a  single  position  of  the  loads  is  sufficient,  but  for  variable 
fixed  concentrated  loads  more  than  one  curve  may  be  required,  as  ex- 
plained on  page  261:  2. 

6.  The  bending  moments  for  a  girder  which  supports  a  uniformly  dis- 
tributed load  vary  as  the  squares  of  the  distances,  and  the  curve  of  mo- 
ments is  a  parabola.    This  is  true  for  moving  loads  as  well  as  for  static 


259 


260 


PART  III  — THE  DESIGN  OF  DETAILS 


loads  because  the  maximum  bending  moment  at  any  point  occurs  when 
the  load  extends  the  entire  length  of  the  girder.  The  vertex  of  the  parab- 
ola is  at  the  center  of  the  span  where  the  bending  moment  is  maximum. 
To  any  convenient  scale,  AB  equal  to  the  half  span  (or  full  span  as  ex- 
plained below)  is  laid  off  horizontally,  and  BC  equal  to  the  total  maxi- 
mum bending  moment  is  laid  off  vertically,  as  in  Fig.  260.  The  vertical 
scale  is  different  from  the  horizontal  scale  because  the  units  are  different. 
It  is  well  to  choose  the  scales  so  that  the  distance  BC  is  no  greater  than 


D' 


£' 


F' 


A'  C 

Fig.  260.    Lengths  of  Cover  Plates  —  Uniformly  Distributed  Loads. 

the  distance  AB  and  no  less  than  three-quarters  of  AB.  With  the  ver- 
tex at  C  a  parabola*  is  drawn  through  A.  The  ordinate  to  the  curve 
from  any  point  between  A  and  B  represents  the  bending  moment  at  that 
point.  On  any  inclined  line  through  B  is  laid  off  BH  equal  to  the  total 

•Construction:  Draw  a  vertical  through  A,  and  lay  off  AA'=  BC.  Divide  AA' 
into  any  number  of  equal  parts,  depending  upon  the  accuracy  required.  Connect  each 
of  these  points  with  C.  Divide  AB  into  the  same  number  of  equal  parts  and  drop  a 
vertical  through  each  point.  The  intersection  of  the  first  vertical  with  the  first  diagonal 
gives  the  first  point  on  the  parabola,  etc.  The  points  may  be  joined  by  means  of  a 
curved  ruler.  Only  enough  of  the  construction  lines  need  be  drawn  to  show  the 
intersections. 


required  net  flange  area  for  which  the  girder  is  designed.  This  is  sub- 
divided so  that  BD  is  the  actual  net  area  of  the  two  flange  angles  together 
with  the  portion  of  the  web,  if  any,  which  is  counted  as  flange  area  in  the 
design,  and  DE,  EF,  FG,  etc.,  are  the  net  areas  of  the  cover  plates,  the 
larger  being  nearer  the  angles.  Usually  the  last  point  will  fall  a  little 
outside  of  the  point  H  because  of  the  excess  in  area  which  results  from 
the  selection  of  commercial  sizes.  A  line  is  drawn  from  H  to  C,  and  lines 
parallel  to  this  line  are  drawn  through  points  D,  E,  and  F.  These  lines 
make  proportionate  intercepts  on  the  line  BC  which  show  the  portion  of 
the  maximum  bending  moment  which  is  resisted  by  each  of  the  com- 
ponent parts,  since  the  net  areas  are  directly  proportional  to  the  bending 
moments  (page  221:2).  Horizontal  lines  drawn  through  these  new 
points  cut  the  parabola  at  points  where  the  corresponding  net  areas 
satisfy  the  bending  moment.  Thus,  from  A  to  D'  the  web  and  the  flange 
angles  are  sufficient  without  cover  plates;  at  D'  the  first  cover  plate  be- 
comes necessary,  but  it  is  not  fully  developed  until  E'  is  reached,  at 
which  point  the  second  cover  plate  begins;  the  third  plate  begins  at  F', 
etc.  The  theoretical  length  of  the  first  (thickest)  plate  is  twice  the  dis- 
tance from  D'  to  B,  the  second  twice  the  distance  E'B,  and  the  third 
twice  F'B.  By  making  AB  equal  to  the  whole  span  instead  of  one-half, 
the  effect  will  be  to  change  the  scale  so  that  the  distances  D'B,  E'B, 
and  F'B  give  the  whole  lengths  of  the  plates  without  doubling.  If  the 
line  BH  is  drawn  so  that  the  line  HC  will  be  horizontal,  the  parallels  will 
be  coincident  with  the  horizontal  lines  which  cut  the  curve,  and  the  con- 
struction is  simplified  (see  illustrative  problem,  page  262: 1).  It  is  often 
more  convenient  not  to  plot  the  bending  moment,  but  to  lay  off  the  net 
areas  along  the  line  BC  and  to  draw  the  parabola  through  the  new  point 
C  =  H .  The  curve  then  represents  net  areas  instead  of  bending  moments, 
and  the  inclined  line  is  not  needed.  It  is  quite  a  common  practice  to 
draw  the  parabola  to  correspond  to  the  point  G  of  the  actual  area  instead 
of  point  H  of  the  required  area.  This  gives  safe  results  but  inconsistent 
results,  because  the  lengths  of  some  cover  plates  may  be  increased  a  foot 
or  more  while  others  in  the  same  girder  are  changed  only  slightly.  It  is 
unnecessary  to  strengthen  the  flange  throughout  its  length  simply  be- 
cause it  happens  to  be  impossible  to  find  a  commercial  size  which  will 
satisfy  the  requirements  at  the  center.  If  all  other  parts  of  the  girder 


CHAPTER   XXXVIII 


COVER  PLATES 


261 


were  strengthened  in  proportion  it  might  be  desirable,  but  even  then  a 
more  equitable  distribution  could  be  devised.  However,  no  great  harm 
can  come  from  the  use  of  actual  areas  instead  of  the  required  areas,  and 
in  some  cases  it  is  more  convenient. 

1.  The  bending  moments  for  a  system  of  concentrated  loads  increases 
constantly  between  loads,  and  the  curve  of  moments  is  a  series  of  straight 
lines.  Since  concentrated  loads  are  found  only  in  conjunction  with  uni- 
formly distributed  loads,  the  two  curves  must  be  combined.  This  may 

_P         P' 


Fig.  261  (a).    Lengths  of  Cover  Plates  —  Combined  Loads. 

be  best  accomplished  by  plotting  one  below  and  the  other  above  a  hori- 
zontal line  so  that  the  combined  ordinates  representing  the  total  bend- 
ing moments  may  be  scaled.  Thus  in  (a) ,  Fig.  261  (a) ,  the  parabola  is  drawn, 
through  P  and  M  so  that  NP  is  the  maximum  bending  moment  due  to 
the  uniform  load,  as  in  the  preceding  paragraph.  The  bending  moment 
due  to  the  concentrated  loads  must  be  found  and  plotted  at  the  point  of 
application  of  each  load,  as  UV  and  NQ.  The  total  maximum  bending 
moment  for  which  the  flanges  were  designed  is  represented  by  the  maxi- 


mum  combined  ordinate  PQ.  This  total  bending  moment  should  be 
subdivided  in  proportion  to  the  resisting  moments  of  the  angles  and  web, 
and  each  cover  plate,  as  in  the  preceding  paragraph.  This  should  be 
done  along  the  edge  of  a  separate  card  or  piece  of  paper,  as  shown  in  (6), 
Fig.  261  (a).  This  card  can  be  made  to  slide  over  the  graph  of  (a),  Fig.  261  (a), 
so  that  P'  follows  the  parabola,  and  the  line  P'Q'  is  kept  vertical.  In  the 
position  where  R'  falls  in  the  lower  curve  at  R,  the  vertical  line  marks  the 
point  where  the  first  cover  plate  should  theoretically  begin,  because  the 
resisting  moment  of  the  angles  and  web  P'R'  satisfies  the  total  bending 
moment  P'R.  Similarly,  the  second  cover  plate  should  begin  where  the 
total  ordinate  P'S  equals  the  distance  P'S',  the  third  where  the  ordi- 
nate P'T  equals  P'T',  etc.  In  case  there  is  no  other  uniform  load  than 
the  weight  of  the  girder  itself,  the  corresponding  bending  moment  would 
be  relatively  so  small  that  the  parabola  would  be  too  flat  to  plot.  In  this 
event  a  single  curve  should  be  plotted  from  the  total  bending  moments. 
Thus  the  bending  moment  due  to  the  concentrated  loads  at  the  point  of 
application  of  each  load  should  be  increased  by  the  bending  moment  due 
to  the  uniform  load  at  the  same  point. 

2.  For  variable  concentrated  loads,  fixed  in  position,  the  lengths  of 
the  cover  plates  are  not  always  determined  from  a  single  position  of  the 
loads.  Take,  for  example,  A  _g 

the  girder  of  a  through  rail- 
way bridge.  The  loads 
should  be  placed  to  give  the 
maximum  bending  moment 
for  which  the  flanges  are 
designed  (page  225  : 1),  the 
total  bending  moment  at 
each  panel  point  should  be 
found  for  this  position  of 
the  loads,  and  the  corre- 
sponding curve  of  bending 
moments  should  be  plotted, 
as  shown  by  the  full  line  in 
Fig.  261  (6).  The  loads  should  then  be  placed  to  cause  the  maximum 
bending  moment  at  one  of  the  other  panel  points,  and  the  curve  of 


L>  aotl  Wet 


Fig.  261  (6).    Lengths  of  Cover  Plates  —  Variable 
Concentrated  Loads. 


262 


PART   III  — THE   DESIGN   OF   DETAILS 


bending  moments  should  be  constructed  for  this  position  in  the  same 
manner,  as  represented  by  the  dashed  line.  Similarly,  a  curve  should  be 
plotted  for  the  position  of  the  loads  which  causes  the  maximum  bending 
moment  at  each  other  panel  point.  Since  the  live  loads  may  cross  the 
bridge  in  either  direction,  the  girder  is  made  symmetrical  and  only  one- 
half  need  be  plotted.  Each  curve  should  be  plotted  for  that  half  of  the 
girder  in  which  the  larger  bending  moments  occur.  Each  curve  will 
be  outside  of  all  the  other  curves  at  least  at  one  panel  point.  The 
maximum  ordinate  BC  representing  the  maximum  bending  moment  for 
which  the  flange  is  designed  should  be  subdivided  as  before  (page  259:  6) 
to  show  the  proportion  of  the  bending  moment  which  is  resisted  by 
each  component  part.  The  length  of  each  cover  plate  is  determined 
by  drawing  a  horizontal  line  through  the  proper  point  on  the  line  BC 
until  it  intersects  the  curve  of  bending  moments  which  is  farthest  from 
the  center.  The  bending  moments  due  to  the  weight  of  the  girder 
are  usually  so  small  that  they  can  be  combined  with  the  bending  mo- 
ments due  to  the  concentrated  loads  which  include  other  dead  loads,  live 
loads,  and  impact.  If  there  were  additional  uniformly  distributed  loads 
it  might  become  necessary  to  plot  the  moment  parabola  separately,  as 
explained  in  the  preceding  paragraph.  There  are  so  many  steps  to  a 
problem  such  as  described  in  this  paragraph  that  inaccuracies  in  computa- 
tion and  in  plotting  are  liable  to  accumulate.  It  is  well,  therefore,  to 
be  somewhat  liberal  in  the  amount  added  to  the  theoretical  lengths  in 
obtaining  the  practical  lengths  to  be  used. 

1.  Illustrative  Problem — Variable  Concentrated  Loads.  —  Find  the 
lengths  of  the  cover  plates  of  the  girder  designed  on  page  225: 1.  The 
maximum  total  bending  moment  at  the  center  was  found  on  that  page  to 
be  3913  thousand  pound-feet,  including  185  thousand  due  to  the  weight 
of  the  girder.  The  concentrated  loads  were  placed  as  shown  in  Fig.  251 
(a).  The  corresponding  bending  moment  at  the  right-hand  quarter  point 
(which  is  greater  than  at  the  left-hand  quarter  point)  is  2769  =  175.4 

410 
X  15  +  -^-  x  15  X  45.     The  full  line  of  Fig.  262  is  plotted  from  these 

m 

bending  moments.  With  the  loads  placed  for  the  maximum  bending 
moment  at  the  quarter  point,  as  in  Fig.  251  (6)  (see  also  page  261:  2),  the 
bending  moment  at  the  center  is  3668  =  194.7  X  30  -  157.2  X  15  +  185, 


and  the  bending  moment  at  the  quarter  point  is  3059  =  194.7  x  15  +  138, 
the  138  being  the  tending  moment  due  to  the  weight  of  the  girder  found 
above.  The  dashed  line  is  plotted  from  these  bending  moments.  On  the 
diagonal  line  are  laid  off  the  total  net  area  40.6  sq.  in.,  the  net  area  of 
the  angles  and  \  of  the  web  17.8  =  13.9  +  3.9,  the  net  area  of  the  14  x  H 
plate  8.2,  and  the  net  areas  of  the  two  14  x  f  plates  each  7.5.  The  total 
area  40.6  is  swung  about  B  as  a  center  until  it  intersects  a  horizontal  line 
through  C.  In  this  way  the  parallel  lines  become  horizontal  and  coinci- 
dent with  the  horizontal  construction  lines  which  cut  the  curves,  which 
may,  therefore,  be  drawn  directly  from  the  points  on  the  diagonal  line 


eo-o 


Fig.  262. 

to  the  curve  farthest  from  the  center  line.  In  this  case  the  lengths  of 
all  three  cover  plates  are  determined  by  the  dashed  line.  Since  the  dis- 
tance AB  was  made  the  full  length  of  the  girder,  the  scaled  lengths  of 
the  cover  plates  represent  the  full  theoretical  lengths.  To  these  should 
be  added  about  three  feet  to  give  the  actual  lengths  to  be  used,  thus: 
46'  0"  =  43.2  +  2.8,  38'  6"  =  35.4  +  3.1,  and  24'  6"  =  21.6  +  2.9.  On  the 
top  flange  the  14  x  yi  plate  should  extend  the  full  length  of  the  girder 
instead  of  46'  0". 

2.  For  a  system  of  moving  concentrated  loads,  such  as  Cooper's  con- 
ventional engine  loads,  it  is  usually  impractical  to  construct  an  accurate 
curve  of  bending  moments  because  this  would  necessitate  finding  the 


CHAPTER   XXXVIII 


COVER  PLATES 


263 


maximum  bending  moments  at  short  intervals,  say  equal  to  the  depth 
of  the  girder.  This  would  involve  a  different  position  of  the  loads  for 
each  bending  moment.  The  resulting  curve  would  approximate  a  parab- 
ola, and  it  is  usually  sufficiently  close  to  consider  it  a  parabola,  provided 
a  liberal  amount  is  added  to  the  length  of  each  plate  to  overcome  the 
discrepancy  between  the  curves.  Usually  from  3  to  4  feet  should  be  added 
to  the  theoretical  length  instead  of  from  2  to  3,  particularly  for  the  short- 
est plate  when  more  than  one  are  used. 

1.  An  algebraic  method  is  more  convenient  than  the  graphic  method 
when  the  curve  of  bending  moments  is  a  parabola.  No  general  algebraic 
method  can  be  given  for  girders  with  fixed  concentrated  loads  because 
the  conditions  are  so  varied.  It  is  possible  to  compute  algebraically  the 
lengths  of  the  cover  plates  for  any  specific  case  by  a  method  adapted  from 
the  corresponding  graphic  method  outlined  in  the  preceding  paragraphs, 
but  this  is  not  usually  recommended  for  fixed  concentrated  loads.  For 
either  'static  or  moving  uniformly  distributed  loads  the  curve  of  maximum 
bending  moments  is  a  parabola,  and  for  moving  concentrated  loads  the 
curve  approximates  a  parabola,  as  explained  in  the  preceding  paragraph. 
The  curve  of  net  flange  areas  is  also  a  parabola  since  the  net  areas  are 
proportional  to  the  bending  moments.  The  equation  of  a  parabola  referred 
to  the  origin  at  the  vertex  is  X2  =  4PF,  which  shows  that  values  of  Y 
vary  as  the  squares  of  the  corresponding  values  of  X,  P  being  a  constant. 

X1        Y  /~F~ 

Hence,  -^r-,  =  -rr  or  X  =  Xi  \/  —  •     Let  us  assume  that  the  parabola  in 
Aj          ti  Y     yt 

Fig.  260  represents  net  areas  instead  of  bending  moments,  and  that  the 
line  BH  coincides  with  BC.  Then  BC  is  the  total  net  area  required,  and 
the  vertex  C  is  the  origin  of  the  coordinates.  Point  A  is  the  only  other 
point  on  the  curve  for  which  the  coordinates  are  known.  Neglecting  the 
signs  because  they  do  not  affect  the  result,  the  coordinates  of  the  point 

A  are  Xi  =  -=>  and   YI  =  a,  where  L  =  the  total  length  of  the  girder,  and 

/  ^ 

a  =  the  total  net  flange  area  required.  If  for  Y  we  substitute  a"  =  the 
distance  from  the  origin  to  the  horizontal  line  which  determines  the  length 
of  any  plate,  then  the  corresponding  value  of  X  will  be  one-half  the  theo- 


retical length  of  that  plate,  or  X  =  -^A/  —  •      On  account  of  the  usual 


excess  of  the  actual  net  area  over  the  required  net  area,  a"  can  be  found 
best  from  a  by  subtracting  the  net  area  of  the  flange  angles,  the  portion 
(if  any)  of  the  web  considered  as  flange  area,  and  the  net  area  of  cover 
plates  between  the  angles  and  the  cover  plate  the  length  of  which  is  de- 
sired. For  the  plate  nearest  the  angles,  a"  is  equal  to  the  net  area  left 
for  cover  plates,  taken  directly  from  the  design  of  the  flange.  The  a" 
for  the  next  plate  is  found  from  this  value  by  subtracting  the  net  area  of 
the  first  plate,  etc.  By  doubling  both  sides  of  the  equation,  we  have 
the  total  theoretical 

length  of  cover  plate  =  L  A/—, 


the  result  being  in  feet  since  L  is  in  feet. 

2.  Illustrative  Problem  —  Uniformly  Distributed  Loads.  —  Find  the 
lengths  of  the  cover  plates  of  the  girder  designed  on  page  222 :  2.  The 
total  net  flange  area  required  is  a  =  30.5.  The  resisting  moment  of  the 
web  was  neglected,  and  the  net  area  of  the  angles  was  15.9.  The  net  area 
of  each  14  x  f  plate  is  7.5.  The  a'  for  the  first  plate  is  14.6  taken  from 
the  design  (30.5  -  15.9).  The  a'  for  the  second  plate  is  7.1  =  14.6  -  7.5. 


The  theoretical   lengths  are  41.5  =  60  /4  and   28.9  =  60 

\     OU.O 

The  actual  lengths  would  be  43'  6",  and  31 '  0"  on  the  bottom  flange.  The 
longer  plate  on  the  top  flange  should  extend  the  full  length  of  the  girder  if 
exposed  to  the  weather. 

RIVETS    IN    COVER    PLATES 

3.  Four  points  must  be  considered  in  determining  the  spacing  of  the 
rivets  which  fasten  the  cover  plates  to  the  flange  angles  of  a  plate  girder. 
These  rivets  must  (1)  transmit  that  part  of  the  total  flange  stress  which  is 
carried  by  the  cover  plates,  (2)  provide  for  the  maximum  increase  in  this 
flange  stress,  (3)  develop  the  strength  of  each  cover  plate  between  the  end 
of  the  plate  and  the  end  of  the  next  plate,  and  (4)  conform  to  the  general 
rules  for  rivet  spacing.  The  first  and  third  points  are  satisfied  when  the 
second  is  provided  for,  and  often  all  requirements  are  fulfilled  when  the 
rivets  are  spaced  according  to  the  usual  rules  for  spacing,  particularly 
those  given  on  pages  69 : 1  (a),  (&),  (d)  and  106 :  2.  Some  companies 
advocate  placing  the  rivets  in  the  cover  plates  opposite  the  flange  rivets 


264 


PART  III  — THE  DESIGN  OF  DETAILS 


through  the  web  in  order  to  simplify  both  the  drafting  and  the  shop  work, 
but  as  a  rule,  the  benefits  derived  do  not  justify  the  use  of  the  large  num- 
ber of  extra  rivets. 

1.  The  rivets  in  the  cover  plates  must  carry  that  proportion  of  the 
increase  in  flange  stress  which  the  net  area  of  the  cover  plates  bears  to 
the  total  net  flange  area.  The  total  increase  in  horizontal  flange  stress 

V 

per  linear  inch  at  any  point  in  the  girder  is  -r-  (page  244:  1)  in  which  V  = 

df 

the  maximum  vertical  shear  for  a  section  at  the  given  point,  and 
dr  =  the  mean  depth  of  the  girder  between  rivet  lines  in  the  vertical  legs 
of  the  flange  angles.  The  portion  of  this  increase  which  is  carried  by  the 

the  net  area  of  all  the  cover  plates  at 


cover  plates  is  —>  in  which  a\ 


the  given  point  and  a  =  the  total  net  flange  area  at  the  same  point  includ- 
ing any  portion  of  the  web  counted  as  flange  area.  The  maximum  pitch 
of  the  rivets  in  the  cover  plates  at  any  point  is  found  by  dividing  r'  =  the 
value  of  one  rivet  in  single  shear  by  this  increase,  or 


ar'  dr 


P 


This  formula  should  be  applied  at  the  theoretical  end  of  each  cover  plate. 
The  resulting  pitches  usually  exceed  6",  so  that  no  further  computations 
need  be  made.  Should  the  pitches  be  considerably  less  than  6",  pitches 
should  be  calculated  at  every  point,  within  the  limits  of  the  cover  plates, 
where  the  pitches  of  the  flange  rivets  through  the  web  are  determined 
(preceding  chapter,  page  241).  The  pitch  in  the  cover  plates  will  always 
exceed  the  corresponding  pitch  of  the  rivets  through  the  web,  but  the 
excess  is  proportionately  less  near  the  center.  If  the  rivets  are  to  be 
placed  opposite  those  in  the  web  the  pitch  need  not  be  computed,  and  if 
placed  opposite  alternate  rivets  in  the  web  only  enough  pitches  need  be 
calculated  to  determine  where  this  double  pitch  is  insufficient. 

2.  Each  cover  plate  should  be  developed  by  rivets  between  the  end  of 
the  plate  and  the  end  of  the  next  plate.  A  plate  which  is  fully  developed 
by  rivets  should  fail  before  the  rivets  when  tested  to  destruction.  A  cover 
plate  in  tension  is,  therefore,  developed  when  there  are  enough  rivets  to 
resist  the  maximum  stress  which  the  plate  will  carry.  This  is  found  by 


multiplying  the  net  area  of  the  plate  by  the  unit  stress  in  tension.  Some 
designers  claim  that  the  plate  should  be  developed  beyond  the  theoretical 
end  of  the  plate,  but  this  is  unnecessary,  as  shown  by  the  curve  of  bend- 
ing moments  in  Fig.  260.  From  the  end  of  the  girder  to  the  point  1  the 
entire  flange  stress  due  to  bending  moment  is  resisted  by  the  angles  and 
the  web.  At  any  point  3  there  is  an  additional  bending  moment  repre- 
sented by  the  distance  2-3.  This  increase  is  provided  for  by  that  part 
of  the  net  area  of  the  plate  represented  by  the  distance  D-4,  and  the  whole 
plate  need  not  be  developed  until  the  point  5  is  reached.  The  increase  in 
flange  stress  is  not  uniform  between  these  points  1  and  5,  but  ample  rivets 
will  be  provided  if  the  pitch  does  not  exceed  the  amount  determined  by 
the  formula  of  the  preceding  paragraph.  Each  plate  extends  one  or  more 
feet  beyond  the  theoretical  end,  and  the  rivets  in  this  extra  length  are 
spaced  not  over  four  diameters  (page  69: 1  (d)).  This  insures  the  de- 
velopment at  any  point  of  at  least  as  much  of  the  plate  as  is  required. 

3.  Illustrative  Problem  —  Uniformly  Distributed  Loads.  —  Find  the 
spacing  of  the  rivets  in  the  cover  plates  of  the  girder  designed  on  page 
222:  2.  •  The  theoretical  lengths  of  the  cover  plates  were  found  on  page 
263:  2  to  be  41.5  and  28.9.  The  maximum  shears  in  thousands  of  pounds 
for  sections  taken  at  the  ends  of  the  cover  plates  may  be  found  from  the 
maximum  end  shear  of  196.8  (page  248: 1)  by  the  approximate  method 

(60  +  41.5V 

and    108.0  =  196.8  X 


(page  247:3)  to  be  140.9  =  196.8  x 
/60  +  28.92 


/60  +  41.5V 


602 


/60  +  28.9V 


602 


The  value  of  one  rivet  in  single  shear  is  r'  =  7.22,  and 


dr  =  65.25.  At  the  end  of  the  first  plate  ai  =  7.5,  and  a  =  23.4  = 
15.9  +  7.5,  the  resisting  moment  of  the  web  being  neglected.  The 
maximum  pitch  determined  by  the  method  of  page  264:  1  is 

23.4  x  7.22  x  65.25 

7.5  X  140.9 
which  exceeds  6".    The  pitch  at  the  end  of  the  second  plate  is 

30.9  X  7.22  x  65.25 
15.0  X  108.0 


CHAPTER  XXXVIII 


COVER  PLATES 


265 


which  also  exceeds  6".  When  the  first  pitch  is  so  large,  as  in  this  case 
10!",  it  is  often  unnecessary  to  find  the  pitch  at  the  ends  of  the  other  plates. 
At  the  ends  of  these  plates  3"  spaces  would  be  used  for  about  1'  9"  =  1J 
X  14"  from  the  actual  ends  (page  69: 1  (d)),  and  6"  spaces  would  be  used 
for  the  remainder. 

1.  Illustrative  Problem  —  Concentrated  Loads.  —  Find  the  spacing  of  the 
rivets  in  the  cover  plates  of  the  girder  designed  on  page  225 : 1.  From 
Fig.  262  it  is  seen  that  the  first  two  plates  end  in  the  first  panel  where  the 
shear  is  nearly  constant.  The  smaller  pitch  will  be  found  in  the  second 

plate  because  the  ratio  —  is  less.     This  pitch  should  be  found  first  for 

if  it  exceeds  6"  it  will  be  unnecessary  to  find  the  pitch  at  the  end  of  the 
longest  plate.  The  maximum  shear  in  thousands  of  pounds  for  a  sedtion 


at  the  end  of  the  second  cover  plate  is  202.0  =  194.7  + 


0.41  X  35.4 


where 


194.7  is  the  maximum  shear  due  to  the  concentrated  loads  (page  250 : 3) 
and  the  second  term  is  a  simplified  expression  equal  to  the  weight  of  the 
girder  (410#/ft)  multiplied  by  one-half  the  length  of  the  cover  plate,  which 
gives  the  shear  due  to  the  weight  of  the  girder.  The  value  of  one  rivet  in 


single  shear  is  r'  =  7.22,  and  dr  =  65.25.     ai  =  15.7  =  8.2  +  7.5,  and  a  =  33.5 

=  15.7  +  13.9  +  3.9.    The  corresponding  pitch  is  4f  =  35-5  X  7.22  x  65.25 

lo.  /  X  ^(JA.O 

Similarly,  the  pitch  at  the  end  of  the  first  cover  plate  is  found  to  be  over 
26.0  X  7.22  x  65.25 


8.2  x  203.6 


The  maximum  shear  for  a  section  at  the  end 


of  the  third  cover  plate  is  88.6  =  164.3  -  80.1  +  °-41  *  2L6    and  the 

• 

,.                              „„      41.0  x  7.22  x  65.25      „ 
corresponding  pitch  is  over  6    =  - — ^r— — — — - The  pitch  at  the 

^•>. J  X  Oo.D 

beginning  of  the  second  panel  would  be  greater  than  at  the  beginning  of 
the  third  cover  plate  because  the  shear  is  only  slightly  greater,  and  the 

ratio  —  is  considerably  greater.    3"  spacing  would  be  used  from  the  actual 

end  of  each  plate  for  a  distance  of  about  1'  9"  (see  preceding  problem), 
and  6"  throughout  the  remainder  of  all  the  cover  plates  except  that  4f " 
must  be  used  for  the  short  distance  from  the  3"  spacing  at  the  end  of 
the  second  plate  to  a  point  beyond  the  entire  connection  of  the  concen- 
trated load  at  the  quarter  point. 


CHAPTER  XXXIX 
WEB  STIFFENERS 

SYNOPSIS:  Stiffening  angles  are  riveted  to  the  web  plate  of  a  girder  wherever  the 
web  plate  is  not  strong  enough  to  resist  the  shearing  stresses.  These  stiffening  angles 
may  serve  incidentally  as  connection  angles. 


1.  The  web  plate'of  a  girder  is  designed  to  resist  all  shearing  stresses. 
The  actual  course  of  the  diagonal  stresses  is  not  known,  but  the  girder  can 
be  designed  to  resist  the  horizontal  and  vertical  components  of  the  shear- 
ing stresses,  because  these  can  be  determined.    The  resistance  of  the  web 
plate  to  the  horizontal  components  was  considered  on  page  255  : 2.     The 
resistance  to  the  vertical  components  only  need  be  discussed  in  this 
chapter. 

2.  Vertical  stiffening  angles  or  "  stiffeners,"  usually  in  pairs,  are  riveted 
to  the  web  plate  of  a  girder  to  assist  in  providing  for  the  vertical  shearing 
stresses  when  the  web  plate  alone  is  not  sufficient  (page  266 :  3).    Stiffen- 
ing angles  are  also  placed  at  concentrated  loads,  serving  either  to  connect 
these  loads  directly  to  the  web,  or  else  to  transmit  to  the  web  any  loads 
which  rest  upon  the  flange.     Stiffening  angles  are  used  at  each  support 
to  transmit  the  entire  reaction,  unless  the  web  plate  is  connected  directly 
to  the  angles  of  a  column  or  other  member.    These  stiffening  angles  may 
serve  as  connection  angles  when  the  girder  is  connected  to  the  face  of 
another  member,  or  they  may  transmit  the  stress  to  the  bearing  when 
the  girder  rests  upon  the  support.    All  stiffening  angles  should  be  accu- 
rately cut  so  that  they  will  fit  tightly  between  the  outstanding  legs  of  the 
top  and  bottom  flange  angles. 

3.  The  thickness  of  the  web  plate  must  be  sufficient  to  satisfy  several 
requirements.     It  should  never  be  less  than  f"  in  a  railway  bridge,  nor 
less  than  ^"  in  a  highway  bridge  or  other  structure.    Many  specifications 
require  that  the  thickness  shall  be  at  least  -fa  of  the  clear  distance  between 


the  flange  angles,  although  this  is  not  so  general  a  requirement  as  some 
others.  It  is  desirable  that  any  plate  over  7  feet  deep  shall  be  at  least 
•iV'  thick  on  account  of  handling  in  the  shop.  The  area  of  cross  section  of 
the  web  plate  at  any  point  must  be  sufficient  to  resist  the  maximum  shear 
for  a  section  at  that  point.  It  is  impractical  to  use  more  than  one  web 
thickness  in  any  girder  on  account  of  the  method  of  construction.  Web 
plates  are  seldom  thicker  than  -fa"  or  f "  for  it  is  better  to  use  reinforc- 
ing plates  where  the  shear  exceeds  a  certain  amount  than  to  use  a  heavier 
plate  throughout  the  whole  length  of  the  girder.  Unless  reinforcing 
plates  are  used,  the  web  thickness  must  be  such  that  the  product  of  the 
gross  area  of  cross  section  (full  depth  times  thickness)  by  the  correspond- 
ing unit  shearing  stress  will  equal  or  exceed  the  maximum  shear  on  the 
girder.  The  gross  area  is  used,  and  the  unit  stress  is  specified  for  the 
gross  section,  because  it  is  not  feasible  to  determine  the  rivet  spacing  in 
the  stiffeners  before  the  web  thickness  is  determined,  and  because  the  use 
of  net  areas  would  not  affect  the  result  appreciably. 

4.  End  stiffening  angles  which  connect  the  web  to  a  supporting  mem- 
ber need  not  be  designed  as  a  whole,  because  the  stress  increments  are 
transmitted  almost  directly  from  the  web  through  the  angles  to  the  sup- 
port, and  at  no  point  do  the  angles  have  to  carry  a  large  cumulative  stress. 
The  lengths  of  the  legs  are  chosen  to  suit  the  conditions  of  each  case, 
usually  from  3  to  6  inches.  The  thickness  is  usually  f "  for  light  girders 
and  -jV'  or  \"  for  heavier  ones.  The  stiffening  angles  over  the  supports  o) 
girders  which  rest  upon  other  members  or  upon  masonry  must  be  designec 


266 


CHAPTER   XXXIX 


WEB  STIFFENERS 


267 


to  transmit  the  entire  reaction.  Since  the  edge  of  the  web  plate  is  not 
flush  with  the  backs  of  the  bottom  flange  angles  and  can  get  no  direct 
bearing,  the  entire  maximum  shear  must  be  carried  from  the  web  plate 
to  the  outstanding  legs  of  the  flange  angles  by  means  of  stiffening  angles. 
These  angles  are  sometimes  placed  at  the  extreme  end  of  the  girder  as  in 
(a) ,  Fig.  267  (a) ,  and  sometimes  so  that  the  outstanding  legs  are  at  the  center 
of  the  bearing  plate,  as  in  (6) ,  Fig.  267  (a).  Angles  placed  at  the  extreme  end 
are  not  so  likely  to  obtain  full  bearing  upon  the  flange  angles,  because 
the  latter  may  be  cut  short  or  damaged  in  cutting.  When  a  girder  rests 
on  top  of  a  column,  or  portion  of  a  column,  the  outstanding  legs  of  the 
stiffeners  should  be  placed  directly  over  part  of  the  main  column  section 
if  practicable.  When  the  reaction  is  too  large  to  be  carried  by  one  pair 
of  stiffeners,  two  pairs  are  used,  as  in  (c)  or  (d),  Fig.  267  (a).  When  the  angles 


(3)  (b)  (c)  (d) 

Fig.  267  (a).  —  Methods  of  Placing  Stiffeners  at  the  Ends  of  Girders. 

are  placed  at  opposite  ends  of  the  bearing  plate,  as  in  (c),  the  pair  nearer 
the  center  of  the  girder  will  get  more  than  half  the  stress  on  account 
of  the  deflection  of  the  girder.  It  is  difficult  to  determine  the  propor- 
tion carried  by  each  pair.  Sometimes  a  beveled  bearing  plate  is  designed 
to  give  an  equal  distribution  under  a  full  load,  but  this  result  is  difficult 
to  accomplish  in  practice.  More  frequently  the  larger  pair  is  assumed  to 
take  two-thirds,  and  the  end  angles  one-third.  This  uncertainty  is  over- 
come by  placing  the  angles  as  in  (d).  Sometimes  more  than  two  pairs  of 
angles  are  required,  as  shown  in  Fig.  101.  The  stiffening  angles  over  the 
support  must  be  designed  to  transmit  the  reaction  by  bearing  on  the  out- 
standing legs  of  the  flange  angles,  which  in  turn  transmit  the  load  to  the 
support.  The  strength  of  the  stiffening  angles  acting  as  a  compression 
member  must  then  be  investigated. 

1.   The  stiffeners  over  the  support  must  be  designed  for  bearing.    The 
angles  are  usually  riveted  against  the  vertical  legs  of  the  flange  angles, 


and  fillers  are  used  between  the  top  and  bottom  flange  angles  to  fill  the 
space  between  the  stiffening  angles  and  the  web,  as  shown  in  Fig.  97. 
In  order  to  place  the  stiffeners  in  this  position  the  ends  must  be  cut  'to 
clear  the  curved  fillet  of  the  flange  angles,  as  shown  in  the  enlarged  sketch 
Fig.  267  (b).  That  part  of  the  stiffeners  which  is  cut  back  in  this  way 
cannot  be  counted  in  bearing,  because  the  usual  shop  methods  do  not 
insure  contact.  Even  if  perfect  contact  were  obtained,  the  value  of  the 
bearing  upon  the  curved  surface  of  the  fillet  would  be  questionable. 
The  fillets  of  6  x  4  and  6x6  flange  angles  are  \"  in  radius,  and  those 
of  8  x  8  angles  are  f ".  Unless  the  stiffeners  are  more  than  -fa"  thicker 
than  the  radius  of  the  fillets,  the  bearing  of  the  web  legs  (i.e.,  the  legs 
riveted  to  the  web)  must  be  ignored,  and  the  portion  of  the  outstanding 
legs  beyond  the  fillets  of  the  flange  angles  must  carry  the  whole  load. 
The  necessary  thickness  of  the  angles  is  found  by  dividing 
the  maximum  reaction  by  the  allowed  unit  stress  in  bearing, 
and  again  by  the  combined  projections  of  the  outstanding  legs 
of  the  stiffeners  beyond  the  fillets  of  the  flange  angles.  If  the 
thickness  of  the  angles  exceeds  the  radius  of  the  fillet  by 
more  than  -fa"  (to  allow  for  inaccurate  cutting),  the  bearing 
of  the  remaining  portion  of  the  web  legs  may  be  counted. 
The  unit  stress  in  bearing  may  be  taken  the  same  as  the  bear- 
ing value  for  pins  and  shop  rivets  (24,000#/  sq.  in.  according  to  the  speci- 
fications of  the  American  Railway  Engineering  Association).  Some 
designers  use  a  smaller  unit  stress  and  count  both  legs  of  the  angles,  but 
it  is  more  logical  to  count  only  that  portion  which  is  sure  to  bear.  The 
outstanding  legs  are  less  likely  to  buckle  when  designed  in  this  manner. 
Some  engineers  design  the  stiffeners  as  compression  members  without 
considering  bearing,  with  the  result  that  the  outstanding  legs  are  often 
seriously  overstressed.  It  is  better  to  design  the  angles  for  bearing,  and 
then  investigate  their  strength  as  a  compression  member.  The  lengths  of 
the  outstanding  legs  are  usually  made  of  the  largest  commercial  sizes  which 
will  not  project  beyond  the  edges  of  the  flange  angles,  but  circumstances 
may  justify  cutting  larger  angles  so  that  they  will  be  flush  with  the  edges 
of  the  flange  angles.  The  web  legs  are  shorter  than  the  outstanding  legs, 
standard  angles  being  used.  The  thickness  should  not  be  less  than  f ", 
and  if  more  than  f"  the  angles  must  be  sub-punched  or  drilled. 


267  (W 


268 


PART  III  — THE  DESIGN  OF  DETAILS 


1.  The  strength  in  compression  of  the  stiffeners  over  the  support  should 
be  investigated.    The  stress  in  the  angles  is  cumulative  throughout  the 
depth  of  the  web,  and  the  full  stress  acts  only  at  the  bottom.    It  is,  there- 
fore, unnecessary  to  consider  the  full  load  acting  at  the  top  of  the  stiffening 
angles,  but  it  is  customary  to  consider  the  length  of  the  compression  mem- 
ber equal  to  one-half  the  depth  of  the  girder.    The  radius  of  gyration  is 
chosen  for  an  axis  through  the  center  of  the  web,  because  the  angles  are 
restrained  in  the  other  direction  by  being  riveted  to  the  web.    Only  the 
area  of  the  angles  is  considered,  the  included  portion  of  the  web  being 
neglected.    The  usual  unit  stress  in  compression  is  used,  as  for  example, 

16,000-70-- 

2.  There  must  be  enough  rivets  in  each  pair  of  stiffening  angles  over 
the  supports  to  transmit  the  whole  stress  taken  by  the  angles.    The  rivets 

which  pass  through  the  flange  angles 
should  not  be  counted  upon  to  take 
any  of  this  vertical  stress,  because  they 
are  fully  developed  in  transmitting  the 
horizontal  stress  from  the  web  to  the 
flange  angles.  The  rivets  are  driven  in 
the  shop,  and  the  value  of  one  rivet  is 
Fig.  268  (a).  limited  by  the  bearing  in  the  web 

(unless  the  double-shear  value  is  less). 

Rivets  which  pass  through  fillers  are  less  effective  than  those  which  connect 
the  parts  directly,  because  the  rivets  are  more  likely  to  bend.  The  usual 
specifications  provide  for  this  by  requiring  arbitrarily  that  the  number  of 
rivets  be  increased  50%  when  they  pass  through  fillers.  Whenever  feasible 
it  is  well  to  increase  the  width  of  the  filler  so  that  some  or  all  of  the  extra 
rivets  may  be  used  to  connect  the  fillers  to  the  web  without  passing 
through  the  angles,  as  shown  in  (a),  Fig.  268  (a).  When  pairs  of  stiffening 
angles  are  close  together  these  fillers  may  extend  under  both  pairs,  as  in 
(6),  Fig.  268  (a).  These  extra  rivets  should  be  spaced  not  more  than  twice 
the  maximum  distance  allowed  in  the  angles,  which  is  sometimes  specified 
5"  instead  of  the  usual  6".  If  the  grip  of  the  rivets  (i.e.,  the  total  thickness 
of  the  parts  connected)  exceeds  four  times  the  diameter,  the  number  should 
be  increased  1%  for  each  additional  sixteenth  of  an  inch  in  the  grip. 


3.  Illustrative  Problem.—  Angles  at  Edges  of  Bearing  Plate.  Design 
the  end  stiffening  angles  of  the  girder  shown  on  page  222 : 2,  arranging 
them  as  in  Fig.  268  (6).  The  outstanding  legs  of  the  flange  angles  are  6",  so 
we  will  use  5  X  3§  stiffeners.  The  maximum  end  shear  was  found  on 
page  248: 1  to  be  196,800#,  and  two-thirds  of  this  will  be  assumed  to  be 
carried  by  the  inner  pair  of  angles.  If  the  angles  are  not  thicker  than 
the  J"  fillet,  the  length  of  bearing  will  be  9"  =  2  (5  -  f),  and  the  correspond- 


ing thickness  must  be  f "  = 


2  x  196,800 


This  is  I"  more  than  the 


" 


3  X  9  X  24,000 

radius  of  the  fillet,  but  if  smaller  angles  were  used  they  would  not  exceed 
the  radius  by  more  than  -fa"  which  is  negligible, 
so  f "  angles  will  be  used.  The  two  angles  are 
separated  by  the  TV  web  and  two  f  "  flange 
angles.  The  half  depth  of  the  girder  is  3  ft. 
From  the  table  on  page  331,  the  safe  load  of 
2  Ls  5  x  3£  x  |  X  3'  0"  is  132,000  when  the 
least  radius  of  gyration  about  an  axis  perpen- 
dicular to  the  web  is  used.  A  larger  safe  load 
determined  by  the  radius  about  the  other  axis 
could  be  used,  because  the  angles  are  restrained, 
but  this  value  need  not  be  found  in  this  case  be- 
cause 132,000  is  equal  to  the  necessary  two-thirds 
of  196,800.  The  number  of  £"  rivets  bearing 
in  the  -fa"  web  plate,  required  in  these  stiff en- 

,      .     , .      2  X  196,800 
ing  angles  is  15  =  ,  and  the  total  number  in  the  angles  an 

2  x  196,800  X  1.5 
3  X  9190 


!E?. 


Fig.  263  (6). 


the  filler  is  22 


Thus  15  rivets  should  be  used  in 


the  angles  *  exclusive  of  the  two  in  the  flange  angles,  and  7  additional 
rivets  should  be  used  in  the  fillers.  The  angles  at  the  end  of  the  girder 
carry  only  one-half  the  load  of  the  angles  just  designed,  so  they  need  be 
only  one-half  as  thick,  the  f"  minimum  being  sufficient.  The  number  of 
rivets  should  be  11  =  22  -=-  2,  but  four  more  are  used  so  that  the  rivets 
line  up  with  those  in  the  other  angles. 

*  Two  more  than  shown  in  Fig.  268  (6). 


CHAPTER   XXXIX 


WEB   STIFFENERS 


269 


1.  Illustrative  Problem  —  Angles  at  Center  of  Bearing  Plate. — -Design 
the  end  stiffening  angles  of  the  girder  designed  on  page  225:  1.  The  maxi- 
mum end  shear  was  found  on  page  250:  3  to  be  207,000$.  The  effective 
length  of  bearing  in  two  5  x  3|  angles  is  9  =  2(5  -  5),  and  the  corre- 

207,000 


spending  thickness  would  have  to  be  1"  = 


Since  no  such 


9  x  24,000 

angles  are  rolled,  and  since  they  would  have  to  be  drilled  if  available,  four 

angles  will  be  used,  each  \"  thick,  arranged  as 
tin  Fig.  269.  The  safe  load  would  be  consider- 
ably greater  than  that  shown  in  the  table  on 
page  331  (see  preceding  problem),  but  for  two 
pairs  of  angles  this  is  2  x  108,000  so  that  no 
further  investigation  is  required.  The  number  of 
I"  rivets  in  each  pair  of  angles,  increased  50% 

207,000  x  1.5 
on  account  of  the  fillers,  is  17  *  =  — ~ — ^— ^ — > 

^  z  x  yiyo 

exclusive  of  those  through  the  flange  angles. 
These  are  all  placed  through  the  angles,  and 
spaced  to  line  up  with  the  rivets  in  the  splice 
plates,  Fig.  273.  Seven-inch  fillers  are  used  ex- 
tending under  both  pairs  of  angles.  If  wider  fillers  were  used,  the  total 
number  of  rivets  would  be  increased  or  else  the  maximum  spacing  would 
be  exceeded. 

2.  Intermediate  stiffeners  are  generally  used  at  concentrated  loads 
and  at  web  splices.  They  are  also  used  in  the  deeper  girders  to  prevent 
the  web  from  buckling  under  its  shearing  stresses.  The  more  modern 
specifications  require  the  use  of  intermediate  stiffeners  when  the  thick- 
ness of  the  web  is  less  than  -Jy  of  the  unsupported  clear  distance  between 
the  flange  angles.  Formerly  some  form  of  "  buckle  formula"  (page  293:  3) 
was  used  to  determine  when  stiffeners  should  be  used.  The  sizes  of 
intermediate  stiffening  angles  are  not  designed,  but  they  are  usually  fixed 
*  Two  more  than  shown  in  the  figure. 


Fig.  269. 


by  the  standards  of  the  different  structural  companies.  The  specifica- 
tions often  require  that  the  length  of  the  outstanding  legs  should  be  at 
least  2"  greater  than  ^V  °f  the  nominal  depth  of  the  girder.  The  inter- 
mediate stiffeners  are  usually  made  lighter  than  the  end  stiffeners,  and 
often  the  legs  are  of  the  next  smaller  commercial  size,  excepting  perhaps 
those  which  serve  as  connection  angles  for  concentrated  loads.  The 
thickness  of  intermediate  stiffening  angles  in  railway  bridges  is  usually 
I",  although  this  may  be  increased  in  the  heavier  girders.  The  thickness 
of  the  intermediate  stiffening  angles  in  other  girders  is  usually  either 
A"  or  |". 

3.  The  spacing  of  intermediate  stiffeners  should  not  exceed  the  maxi- 
mum allowed  by  different  clauses  in  the  specifications.     The  stiffeners 
at  concentrated  loads  are  usually  fixed  in  position.    In  railway  bridges, 
viaducts,  and  heavy  crane  runways,  the  clear  distance  between  stiffeners 
should  never  be  more  than  6  feet,  nor  more  than  the  clear  distance  be- 
tween the  flange  angles;  it  should  not  exceed  27;  (12,000  -  v),  in  which 

t  =  the  thickness,  and  v  =  the  maximum  shear  intensity,  in  pounds  per 
square  inch  of  gross  section.  This  formula  provides  for  closer  spacing  near 
•the  ends  of  the  girder  where  the  shear  intensity  is  greater.  In  highway 
bridges  and  structures  other  than  those  mentioned  above,  the  clear  distance 
between  stiffeners  should  not  exceed  5  feet,  nor  the  full  depth  of  the  web. 

4.  The  number  of  rivets  in  intermediate  stiffeners  is  not  computed,  but 
the  rivets  are  made  to  line  up  with  those  in  the  stiffeners  at  the  supports. 
This  simplifies  both  the  drafting  and  the  shopwork,  particularly  when 
multiple  plate  punches  are  used.    The  full  number  is  used  in  the  stiffeners 
at  concentrated  loads  and  at  splices,  but  in  other  stiffeners  the  alternate 
rivets  may  be  omitted  if  the  resulting  spaces  do  not  exceed  the  allowed 
maximum.     Care  should  be  taken  to  see  that  the  number  of  rivets  in 
stiffeners  used  as  connection  angles  fully  provide  for  the  loads. 

5.  Intermediate  stiffening  angles  which  have  no  connections  to  the 
outstanding  legs  may  be  crimped,  as  explained  on  page  97: 1. 


CHAPTER  XL 
SPLICES 

SYNOPSIS:   The  design  of  typical  splices  is  illustrated  by  different  types  of  girder 
and  column  splices. 


1.  Definition.  —  One   member   is   usually   connected   to   another   by 
means  of  connection  plates  or  angles,  but  a  member  or  part  of  a  member 
is  said  to  be  spliced  when  the  two  similar  segments  are  connected  end  to 
end  in  the  form  of  a  butt  joint.     A  splice  becomes  necessary  when  the  de- 
sired length  of  material  is  not  available,  or  when  it  is  impracticable  to  ship  a 
whole  member  in  one  piece.     Whenever  possible  a  splice  should  be  avoided. 

2.  Design.  —  A  splice  should  be  designed  to  transmit  the  full  stress 
in  the  part  spliced.     In  a  tension  member  or  a  light  compression  mem- 
ber the  splice  plates  or  angles  should  be  designed  to  carry  the  full  stress. 
This  is  not  feasible  in  a  heavy  column  or  chord  member,  so  part  of  the 
stress  is  transmitted  by  direct  bearing,  the  ends  of  the  two  segments 
being  "milled"  or  "faced"  (page  31: 1)  to  furnish  uniform  bearing  against 
each  other,  as  shown  in  Figs.  124  and  133.     The  rivets  in  each  half  of  the 
splice  plates  or  angles  should  fully  develop  that  part  of  the  stress  which 
is  carried  by  the  corresponding  plates  or  angles.     Thus  in  a  tension  mem- 
ber, the  combined  net  areas  of  the  splice  plates  or  angles  should  equal 
or  exceed  the'  net  area  for  which  the  main  member  is  designed,  as  illus- 
trated by  the  problems  on  page  208:  4,  and  the  rivets  which  connect  the 
splice  plates  or  angles  to  each  segment  should  develop  the  full  strength 
of  the  main  member.     In  a  milled  splice  of  a  heavy  compression  member 
most  of  the  stress  is  transmitted  by  direct  bearing,  but  enough  splice 
plates  or  angles  should  be  used  to  hold  the  segments  in  the  proper  posi- 
tion and  to  transmit  the  stresses  due  to  bending. 

3.  Three  types  of  splice  are  selected  to  illustrate  the  principles  em- 
bodied in  the  design  of  any  ordinary  splice.     These  three  will  be  dis- 


cussed in  the  following  order:  a  splice  in  the  web  of  a  plate  girder,  a  splice 
in  the  flange  of  a  plate  girder,  and  a  column  splice. 

WEB   SPLICES 

4.  When  Used.  —  The  web  plates  of  all  girders  over  40  or  50  feet  long 
must   be    spliced    because  longer   plates  are  not   rolled.    The   extreme 
lengths  of  some  of  the  deeper  webs  are  less  than  20  feet  so  that  the  webs 
of  the  longer  girders  must  be   spliced  at  several  points.     The  number 
of  splices  is  determined  by  the  maximum  rolled  lengths  *  of  the  plates, 
but  for  convenience  in  handling  the  plates  in  the  shop  no  single  plate 
should  weigh  more  than  3000#.     A  splice  should  not  be  located  at  the 
point  of  maximum  bending   moment,  except  possibly  in  comparativelj 
light  girders  which   would  then   require  only  one  splice.     It  is  usuallj 
customary  to  locate  each  splice  under  a  pair  of  stiffening  angles.     Nol 
only  is  the  splice  thus  stiffened,  but  the  thickness  of  the  fillers  is  reduced 
and  there  is  one  less  line  of  rivets  to  be  driven. 

5.  The  design  of  a  web  splice  depends  upon  the  method  by  which  th< 
girder  is   designed,   because   the  splice   plates   must   transmit   the  wel 
stresses.     If  the  entire  flange  stress  is  considered  to  be  resisted  by  th< 
flange,  and  the  resisting  moment  of  the  web  plate  is  neglected  (as  in  Casi 
A,  page  221:  2),  the  splice  is  designed  for  shearing  stresses  only.     If  tb 
resisting  moment  of  the  web  isconsidered  (as  in  Case  B,  page  223:  2),  th 
splice  must  be  designed  for  stresses  due  both  to  shear  and  to  bendin] 

*  See  Ketchum's  "Structural  Engineers'  Handbook,"  McGraw-Hill  Book  Co.,  Inc 
New  York,  or  the  handbooks  of  steel  manufacturers. 


270 


CHAPTER   XL 


SPLICES 


271 


moment.  When  there  are  more  than  two  splices  in  a  girder,  the  one 
'or  which  the  shear  is  greatest  is  designed  and  the  others  are  made  like 
for  practical  advantages  during  fabrication.  Splice  plates  are  placed 
on  both  sides  of  the  web,  and  the  thickness  of  each  plate  should  not  be 
.ess  than  |"  in  railway  bridges  or  TV  in  other  structures. 

1.  When  the  splice  is  designed  for  shear  only  the  plates  extend  the 
'ull  depth  between  flange  angles,  except  for  a  clearance  of  j"  (or  less) 
at  each  end,  being  the  same  length  as  the  fillers  (page  96:  4).  The  net 
area  of  the  two  splice  plates  in  a  vertical  cross  section  should  be  as  great 
as  the  net  area  of  the  web  plate,  but  for  all  practical  purposes  it  is  close 
gnough  to  compare  the  gross  areas  since  the  proportions  are  so  nearly 
identical.  The  width  of  the  splice  plates  is  determined  by  the  spacing  of 
:he  rows  of  rivets  which  often  depends  upon  the  size  of  the  superimposed 
stiffening  angles.  A  space  of  from  \"  to  f  "  is  usually  left  between  the  two 
sections  of  the  web  (page  96 : 2) .  At  least  two  rows  of  rivets  are  com- 
monly used  in  each  half,  even  though  one  row  would  satisfy  the  con- 
ditions. Usually  the  rivets  in  the  inner  rows  are  spaced  like  those  in  the 
intermediate  stiffening  angles  (page  269:4),  but  those  in  the  outer  rows 
are  spaced  twice  as  far  apart.  After  the  rivets  have  been  located  in 
i  this  manner  their  resistance  to  shear  should  be  investigated.  The  shear, 
or  the  algebraic  sum  of  the  vertical  external  forces  on  one  side  of  the 
lice,  is  positive,  while  the  shear  on  the  other  side  is  of  equal  magnitude 
but  negative,  in  order  to  satisfy  the  V  equation  of  equilibrium.  Since 
the  shearing  stresses  are  transferred  from  one  segment  of  the  web  to 
;he  other  by  means  of  the  splice  plates  and  the  rivets,  the  effect  is  the 
e  as  if  the  maximum  shear  V  were  a  single  resultant  force  acting 
upward  at  the  center  of  gravity  of  the  group  of  rivets  in  one-half  the 
splice,  with  an  equal  downward  resultant  force  acting  at  the  center  of 
gravity  of  the  rivets  in  the  other  half.  A  couple  is  thus  formed,  the 
moment  of  which  is  the  product  of  a  single  force  V  by  the  perpendicular 
listance  between  the  two  forces.  This  moment  tends  to  cause  rotation 
>f  the  splice  plates,  and  the  splice  is  a  double  eccentric  connection.  The 
ivets  in  each  half  of  the  splice  must  not  only  satisfy  the  maximum  ver- 
ical  shear  V,  but  they  must  resist  one-half  of  this  moment  according 
o  the  method  of  eccentric  connections,  page  237  :  2.  Should  the  strength 
<f  the  rivets  prove  to  be  insufficient,  the  number  in  the  outer  row  may 


'-£' 


be  increased  by  one  or  more,  the  number  in  the  inner  row  may  be  made 
the  same  as  the  rivets  in  the  end  stiffeners  if  not  already  the  same,  the 
rows  may  be  spread  slightly,  or  the  number  of  rows  may  be  increased. 

2.  Illustrative  Problem  —  Web  Splice  for  Shear  Only.  —  Design  a 
splice  for  the  web  at  the  quarter  point  of  the  girder  shown  on  page  222 :  2. 
The  maximum  shear  for  a  section  at  the  quarter  point  in  thousands  of 
pounds  may  be  found  from  the  maximum  end  shear  by  the  approximate 
method  (page  247:  3)  to  be  110.7  =  196.8  x  (f)2.  The  length  of  the  splice 
plates  is  60"  =  72.5  -  2(6  +  J),  and  the  thickness  of  each  plate  is  found 
by  equating  the  gross  area  of  two  splice  plates  to  the  gross  area  of  the 
web  plate  thus:  2  x  60<  =  72  x  f^;  this  gives 
a  value  for  I  less  than  the  minimum,  so  f " 
plates  are  used.  The  minimum  number  of 
rivets  is  as  shown  in  Fig.  271,  the  spacing 
in  the  intermediate  stiffeners  being  the  same 
as  in  the  end  angles  shown  in  Fig.  268  (V) 
because  the  double  pitch  would  exceed  the 
maximum  allowed.  Since  the  inner  row  has 
approximately  twice  as  many  rivets  as  the 
outer  row,  the  center  of  gravity  may  be 
taken  one-third  of  the  distance  from  the 
inner  row  to  the  outer  row.  The  distance 
from  this  center  of  gravity  to  the  center  of 
the  splice  is  3"  =  1  +  2,  which  is  half  the 

distance  between  the  centers  of  gravity  of  the  two  groups  of  rivets. 
The  half  moment  of  the  couple  is  then  332,100#/  in.  =  110,700  x  3. 
The  sum  of  the  squares  of  the  horizontal  and  vertical  distances  to 
the  rivets  is  6670  =  7  x  22  +  13  x  I2  +  4(9J2  +  192  +  28£2)  +  2(4 J2  +14»2 
+  23 j2).  The  coordinates  of  the  rivet  farthest  from  the  center  of  rotation 
are  xm  =  1,  and  ym  =  28£.  The  horizontal  component  of  the  shearing 


m 


Fig.  271. 


forces  on  the  critical  rivet  is  1420#  = 


332,100  X28.5 


and  the  vertical 


*  •    KCWM      110,700      332,100  X  1 
component  is  5850#  =  — ^ (- 


20 


6(570 


6670 

•    The  resultant  of  these  two 


components  is  obviously  less  than  9190#,  the  value  of  a  £"  rivet  bearing 
in  a  TV  web,  so  no  more  rivets  need  be  added. 


272 


PART  III— THE   DESIGN   OF  DETAILS 


1.  When  the  splice  is  designed  for  bending  moment  as  well  as  for 
shear  the  same  plates  may  serve  to  resist  both,  or  separate  plates  near 
the  flange  may  be  used  to  resist  the  bending  moment,  as  explained  in 
the  next   paragraph.     The  portion  of  the  bending  moment  which  is  re- 
sisted by  the  web  may  vary  somewhat  on  account  of  the  abrupt  change 
in  flange  area  at  the  ends  of  the  cover  plates,  but  the  splice  should  be 
designed  to  transmit  the  full  resisting  moment  of  the  web  plate.     This 
resisting  moment  at  any  point  in  the  girder  is  found  by  multiplying  f  of 
the  gross  area  of  the  web  plate  (or  other  portion  used  in  designing  the 
flange)  by  the  unit  stress  hi  bending  and  by  the  effective  depth  of  the 
girder  from  center  to  center  of  gravity  of  the  flanges  (page  224: 1).     When 
only  one  pair  of  splice  plates  is  used,  their  section  modulus  as  well  as 
the  area  of  cross  section  of  the  plates  should  equal  or  exceed  that  of  the 
web  plate.     Thus,  the  square  of  the  depth  of  the  splice  plates  multiplied 
by  then-  combined  thickness  should  not  be  less  than  the  square  of  the 
depth  of  the  web  plate  multiplied  by  the  web  thickness.     The  strength 
of  the  rivets  in  each  half  of  the  plates  should  be  investigated  in  the  same 
manner  as  those  in  a  splice  designed  for  shear  only  (see  above)  except 
that  they  must  resist  not  only  the  vertical  shear  and  the  half  moment 
due  to  shear,  but  they  must  also  resist  the  full  resisting  moment  of  the 
web  as  described  in  this  paragraph.     Although  the  full  resisting  moment 
of  the  web  is  not  always  developed  at  the  same  time  that  the  maximum 
shear  exists,  it  is  customary  to  design  the  splice  as  if  the  two  maximums 
occurred    simultaneously.     This   type   of   splice   is   sometimes   rendered 
more  effective  by  spacing  the  rivets  closer  together  near  the  flanges  than 
near  the  neutral  axis.     When  this  is  done,  the  rivets  in  all  the  stiffening 
angles  should  be  spaced  accordingly. 

2.  Separate -splice  plates  may  be  designed  to  resist  that  part  of  the 
bending  moment  carried  by  the  web  when  the  single  pair  of  plates  de- 
scribed in  the  preceding  paragraph  prove  unpractical.     Sometimes  these 
additional  plates  are  placed  against  the  vertical  legs  of  the  flange  angles,* 
but  more  frequently  the  central  plates  are  cut  short  and  the  additional 
plates  are  placed  between  them  and  the  angles,  as  shown  in  Fig.  272. 

*  See  Kunz's  "Design  of  Steel  Bridges,"  McGraw-Hill  Book  Co.,  Inc.,  New  York, 
or  Johnson-Bryan-Turneaiire's  "Modern  Framed  Structures,"  Part  III,  John  Wiley  and 
Sons,  Inc.,  New  York. 


These  additional  plates  are  designed  to  resist  the  bending  moment,  and 
the  central  plates  are  designed  to  resist  the  shear.  The  former  must  be 
designed  first  because  their  width  determines  the  length  of  the  central 
plates.  Usually  a  clearance  of  \"  (or  less,  page  96  :  4)  is  left  between  the 
shear  and  the  moment  plates,  and  between  the  moment  plates  and  the 
flange  angles.  The  resisting  moment  of  the  two  sets  of  moment  plates 
must  equal  or  exceed  the  resisting  moment  of  the  web  plate  found  as 
explained  in  the  preceding  paragraph.  The  distance  from  center  to  center 
of  splice  plates  ds  is  considerably  less  than  the  effective  depth  of  the  gir- 
der da,  as  shown  in  Fig.  272.  For  the  same  unit  stress,  the  product  of  the 
net  area  of  one  pair  of  splice  plates  by  the  distance  d,  must  equal  the 
product  of  I  the  gross  area  of  the  web  by  the  depth  ds,  or  the  net  area 
of  one  pair  of  splice  plates  must  be  at 

least  -f-  times  the  |  (or  other  portion) 


Fig.  272. 


of  the  gross  area  of  the  web  considered 
as  flange  area.  The  width  of  the 
splice  plates  depends  upon  the  num- 
ber and  the  spacing  of  the  rows  of 
rivets.  A  trial  design  may  be  made 
with  8"  or  9"  plates  allowing  for  three 
rows  of  rivets  spaced  2|"  or  3"  apart. 
The  combined  thickness  of  the  mo- 

ment plates  is  found  by  dividing  the  net  area  by  the  net  width.  Nc 
plate  should  be  thicker  than  the  flange  angles.  The  number  of  rivets 
in  each  half  should  be  sufficient  to  fully  develop  the  tensile  strengtt 
of  the  plates  selected,  at  the  same  unit  stress  for  which  the  flange  wa; 
designed.  The  length  of  the  plates  depends  upon  the  number  and  th< 
spacing  of  the  rivets.  The  rivets  may  be  placed  opposite  (thus  makinj 
the  plates  shorter)  or  staggered  (making  the  plates  thinner)  ,  as  best  suit; 
the  superimposed  stiffeners.  The  proportions  may  be  changed  if  desirec 
by  changing  the  number  of  rows  of  rivets.  After  the  moment  plates  ar 
determined,  the  central  shear  plates  may  be  designed  in  the  same  manne 
as  on  page  271  :  1,  the  gross  area  of  the  two  plates  being  as  large  as  the  gros 
area  of  the  whole  web,  and  the  strength  of  the  rivets  being  sufficient  t 
resist  both  the  direct  shear  and  the  resulting  moment  due  to  eccentricity. 


, 


CHAPTER   XL 


SPLICES 


273 


1.  Illustrative  Problem  —  Web  Splices  for  Moment  and  Shear.  —  De- 
sign a  splice  for  the  girder  shown  on  page  225 : 1,  assuming  the  web  to  be 
cut  into  three  lengths  of  about  20  feet.  Assume  9"  moment  plates  with 
three  rows  of  rivets,  as  shown  in  Fig.  273. 

72.3"  =  effective  depth  da  (page  225  :  1) 
51.0"  =  72J  -  2(6  +  i)  -  9  =  d,  =  distance  c.  to  c.  of  splices 
3.9  sq.  in.  =  |  of  the  gross  area  of  the  web  (page  225  : 1) 

72.3  X  3.9 


2120# 


7   "   _ 

Tff      - 


51.0  X  2  (9  -  3  x  1) 


thickness  of  each  moment  plate 


84,000#  =  2  x  6  x  TV  x  16,000  =  developed  strength  of  two  plates 
10  =  number  of  |"  rivets  bearing  in  -fa"  web  (page  310). 

These  rivets  may  be  satisfactorily  arranged  as  in  the  figure,  so  no  change 

need  be  made  in  the  number  of  rows. 

41.5"  -  51.0  -9-2x1-  depth  of 
the  central  shear  plates 

3,,      72  x  T 


322  3 


2  x  41.5 


required  thickness 


Fig.  273. 


of  each  shear  plate.  This  is  so  nearly 
equal  to  the  thickness  of  the  moment 
plates  that  it  would  be  increased  to  Ty 
so  that  the  fillers  under  the  stiffening 
angles  may  extend  over  all  the  splice 
plates.  The  vertical  spacing  of  the  rivets 
is  arranged  as  shown  to  accommodate 
both  the  splices  and  the  stiffening  angles 
(page  269  :  1).  Alternate  rivets  are 
omitted  in  the  outer  rows  of  the  central  plates,  and  the  strength  of  the 
remaining  rivets  is  investigated  as  on  page  271  :  2.  The  distance  from  the 
center  of  gravity  of  the  rivets  to  the  center  of  the  splice  is  3"  as  in  the 
preceding  problem. 

88,300#  =  90,400  -  410  x  5  =  maximum  shear  (page  250  :  3) 
2410    =  5x22  +  9xl2  +  4(102  +  19i2)  =  2(52  +  152)  =  sum  of  squares 


88,300  x  3  x  19.25 
2410 


hor.  comp.  on  critical  rivet 


fi.     „      88,300  ,  88,300  x  3  x  1 

— j^ —  ^ 2410 —  —  V        coraP-  on  critical  rivet 

The  resultant   of  these  components  is  obviously  less  than  9190#,  the 
value  of  a  £"  rivet  bearing  in  a  ^"  web,  so  the  splice  is  satisfactory. 

FLANGE  SPLICES 

2.  When  Used.  —  Flange   splices  should   be   avoided   wherever   pos- 
sible.    Cover  plates  more  than  80  feet  long  must  be  spliced;  6x6  flange 
angles  are  rolled  in  some  mills  *  up  to  100  feet  in  length,  and  8x8  angles 
up  to  120  feet.     Special  arrangements  may  be  made  for  rolling  longer 
angles,  and  it  is  often  better  to  pay  the  extra  cost  than  to  splice  the  angles. 
When  bridge  girders  are  built  with  curved  ends,  as  in  Fig.  101,  it  is  im- 
practical to  bend  the  long  flange  angles  or  cover  plates  and  they  should 
be  spliced  near  the  curves.     Most  flange  splices  are  made  in  the  shop, 
because  most  girders  are  shipped  complete  as  single  members.     Girders  for 
export,  or  girders  which   have  to  be  hauled  through  crowded  streets, 
may  have  to  be  shipped  in  sections  and  joined  at  the  site  in  order  to  meet 
the  shipping  requirements. 

3.  No  two  component  parts  of  a  girder  should  be  spliced  at  the  same 
point  (except  as  provided  on  page  274  :  3)  and  preferably  not  within  2  feet 
of  each  other  so  that  the  stresses  can  properly  readjust  themselves  be- 
tween splices.     It  is  usually  permissible  to  splice  a  top  angle  vertically 
over  a  bottom  angle  provided  they  are  on  opposite  sides  of  the  web.     In 
order  to  keep  the  spacing  symmetrical,  the  remaining  angles  are  usually 
spliced  at  an  equal  distance  the  other  side  of  the  center  line.     Angle 
splices  should  preferably  be  placed  where  there  is  an  excess  in  flange 
area,  i.e.,  near  the  end  of  a  cover  plate  which  is  not  used  as  a  splice  plate. 
Flange  splices  are  usually  made  without  .clearance  between  the  ends  of 
the  spliced   plates  and   angles  for  the  sake  of  stiffness,   but   the  ends 
cannot  be  milled  after  assembling  and  it  is  difficult  to  obtain  perfect 
bearing.     The  splice  of  a  compression  flange  is  therefore   made   like  a 

*  See  Ketchum's  "Structural  Engineers'  Handbook,"  McGraw-Hill  Book  Co.,  Inc.,. 
New  York.  — 


274 


PART   III  — THE   DESIGN   OF  DETAILS 


spike  for  a  tension  flange,  no  allowance  being  made  for  the  direct  bear- 
ing of  the  abutting  ends. 

1.  A  cover  plate  is  spliced  usually  at  the  point  where  another  cover- 
plate  would  otherwise  end,  so  that  the  latter  may  be  extended  to  serve 
as  a  splice  plate.     In  this  way  less  material  and  fewer  rivets  are  required 
than  if  a  separate  splice  plate  were  used.     At  this  point  of  splice  one 
continuous  plate  is  cut,  and  another  plate  begins.     In  effect  this  means 
that  the  stress  in  the  single  plate  on  one  side  of  the  splice  must  be  trans- 
mitted to  one  of  the  two  plates  on  the  other  side,  but  to  which  one  is 
immaterial  provided  the  net  area  is  the  same.     It  simplifies  the  analysis 
to  consider  that  the  stress  is  imparted  to  the  outer  plate,  although  the 
actual  distribution  of  the  stress  between  the  two  plates  does  not  affect 
the  result.     The  outer  plate  may  be  extended  beyond  the  splice  to  form 
a  lap  joint  with  the  single  plate,  enough  rivets  being  used,  acting  in  a  single 
shear,  to  fully  develop  the  plate.     The  rivets  are  usually  spaced  about 
3"  apart  to  reduce  the  length  of  the  outer  plate.     The  splice  is  thus  com- 
pleted on  one  side  of  the  original  point  of  splice.     The  remaining  section 
of  the  cut  plate  is  considered  to  act  as  the  new  plate  which  begins  at  the 
point  of  splice,  and  the  rivets  should  be  spaced  close  together  for  the 
usual  distance  from  this  end  (page  69 : 1  (d)). 

2.  A  flange  angle  is  spliced  by  means  of  a  "cover  angle"  or  "splice 
angle"  the  vertex  of  which  must  be  cut  to  fit  the  curved  fillet  of  the 

flange  angle,  as  shown  in  Fig.  274.  The  legs  of  these 
angles  are  cut  so  the  edges  will  be  approximately  flush 
with  the  nominal  edges  of  the  flange  angles.  Special 
gages  are  usually  required  to  give  the  necessary  driving 
clearance.  If  possible,  the  net  area  of  the  splice  angle 
should  be  as  large  as  the  net  area  of  the  flange  angle, 
otherwise  the  deficiency  must  be  made  up  by  a  plate 
riveted  to  the  opposite  flange  angle,  as  shown  in  the  figure. 
The  net  area  of  the  splice  angle  is  the  product  of  the  thickness  by  the 
value  found  by  subtracting  the  thickness  of  the  angle  and  the  diameter 
of  each  hole  in  any  one  crosssection  (usually  two,  page  221  :  2)  from  the 
sum  of  the  two  cut  legs.  No  consideration  need  be  made  of  the  part 
of  the  angle  which  is  cut  away  to  clear  the  fillet  of  the  flange  angle  be- 
cause this  is  compensated  for  by  the  fillet  of  the  splice  angle  itself.  The 


Fig.  274. 


rivets  in  each  half  of  the  splice  angle  must  fully  develop  the  splice  angle. 
The  same  flange  rivets  which  are  used  to  transmit  the  flange  stress  from 
the  web  to  the  flange  angles  may  be  counted  for  this  purpose  because 
the  shearing  plane  is  on  the  opposite  side  of  the  flange  angle.  The  stress 
developed  in  each  rivet  between  the  web  and  the  flange  angles  depends 
upon  the  double  shear  value  or  the  bearing  value  in  the  web,  whichever  is 
smaller.  One-half  of  this  value  represents  the  stress  in  the  plane  between 
the  web  and  one  flange  angle.  This  amount  should  be  subtracted  from 
the  bearing  value  in  the  flange  angle  to  show  the  bearing  value  available 
in  the  plane  between  the  flange  angle  and  the  splice  angle.  This  differ- 
ence should  be  compared  with  the  single  shear  value,  and  the  smaller 
taken  as  the  limiting  value  of  each  rivet  through  the  web  leg.  Usually 
the  flange  angles  are  so  thick  that  the  full  single  shear  value  may  be  used. 
This  is  especially  true  when  extra  rivets  are  used,  i.e.,  when  the  spacing 
is  less  than  the  pitch  determined  by  the  flange  stress.  The  limiting 
value  of  each  rivet  through  the  outstanding  leg  will  be  the  single-shear 
value,  even  though  cover  plates  are  connected  by  the  same  rivets.  If  a 
splice  plate  is  used  on  the  opposite  side  of  the  flange  to  supplement  the 
splice  angle,  the  number  of  rivets  in  the  plate  is  determined  independently. 
If  the  plate  were  in  contact  with  the  angle  to  be  spliced,  the  value  of  each 
rivet  would  be  the  same  as  that  in  the  web  leg  of  the  splice  angle,  and  a 
corresponding  number  of  rivets  should  be  found  which  would  fully  de- 
velop the  splice  plate.  However,  this  number  must  be  increased  by 
885%  for  each  intervening  plate  according  to  the  usual  specification  for 
indirect  splices.  If  there  are  no  vertical  flange  plates,  the  web  and  the 
continuous  flange  angle  make  two  intervening  "plates."  Splices  are 
usually  made  as  short  as  practical  by  spacing  the  rivets  3"  apart,  or  less,  a 
due  consideration  being  given  to  the  minimum  spacing  allowed  (page 
255 :  2).  Flange  splices  should  logically  be  placed  in  a  panel  between 
stiffening  angles  so  they  will  not  interfere  with  the  stiffeners. 

3.  The  splice  at  the  curved  end  of  the  top  flange  of  a  girder  occurs 
where  there  is  a  large  excess  of  flange  area,  especially  when  the  cover 
plate  extends  to  the  end.  It  is  therefore  permissible  to  cut  both  flange 
angles  at  the  same  point  in  this  case,  and  it  is  usually  unnecessary  to 
fully  develop  the  angles  or  the  plate,  provided  the  splices  are  designed 
to  safely  carry  the  maximum  stresses  which  can  reach  them.  Such 


CHAPTER   XL 


SPLICES 


275 


splices  are  shown  in  Fig.  101.  When  the  whole  reaction  is  carried  by 
stiffening  angles  placed  at  the  center  of  the  bearing,  end  angles  may  be 
used  with  a  small  curve  at  the  top  which  extends  only  to  the  main  stiffen- 
ers,  meeting  the  main  flange  angles  at  that  point,  as  shown  in  Fig.  21. 
No  splice  is  necessary,  and  smaller  angles  may  be  used  since  their  prin- 
cipal function  is  to  improve  the  appearance  of  the  end  of  the  girder.  The 
end  cover  plate  should  be  of  the  same  width  as  the  top  plate. 

1.   When  a  field  splice  becomes  necessary  it  should  be  made  as  com- 
pact as  possible  in  order  to  reduce  the  number  of  field  rivets  and  the 

19  ft/Veto  Req'd 


7  Rirets  Req'd 


7  Rivets  Req'd 


Fig.  275.     Typical  Field  Splice  in  a  Girder  Flange. 


nearer  the  center  of  the  girder  being  located,  if  possible,  at  a  point  where 
the  third  cover  plate  may  be  extended  to  serve  as  a  splice  plate.  The 
net  area  of  each  splice  angle  is  usually  about  three-fourths  of  the  net 
area  of  one  flange  angle.  It  is  considered  good  practice,  in  order  to  stiffen 
the  whole  splice,  to  place  enough  rivets  through  the  vertical  legs  of  the 
flange  angles  between  the  two  splices  to  develop  one  flange  angle.  Thus 
a  lap  joint  is  formed  which  transmits  the  stress  of  one  flange  angle,  and 
the  splice  angles  need  carry  only  the  stress  of  the  other  flange  angle.  No 
excess  need  be  added  on  account  of  the  web  intervening,  because  the 

number  of  rivets  determined  by  the 
single-shear  value  together  with  the 
rivets  in  the  outstanding  legs  will 
be  more  than  would  be  required 
for  two  independent  splices.  The 
rivets  in  both  legs  of  the  splice 
angles  beyond  each  splice  is  deter- 
mined by  the  number  in  single  shear 
required  to  develop  the  splice  angle 
next  to  the  flange  angle  which  is 
spliced.  At  least  as  many  of  these 
rivets  should  be  placed  in  the  web 
leg  as  are  required  to  transmit  the 
remaining  stress  to  the  opposite 
splice  angle,  allowing  two-thirds  ex- 
cess on  account  of  the  intervening 
web  and  flange  angle.  The  splice 


lengths  of  the  different  sections  of  the  girder.  Some  specifications  re- 
quire that  no  two  splices  in  a  flange  shall  be  within  two  feet  of  each  other 
but  this  requirement  would  make  a  field  splice  much  longer  than  seems 
to  be  necessary.  A  typical  flange  splice  is  shown  in  Fig.  275.  The  web 
is  spliced  as  explained  in  the  first  part  of  this  chapter.  One  angle  is 
spliced  to  the  left  of  the  web  splice  and  the  other  to  the  right,  two  splice 
angles  of  equal  length  being  used  for  both  splices.  For  convenience,  the 
rivets  in  the  two  legs  are  placed  opposite.  One  cover  plate  is  spliced  at 
the  left  end  of  the  splice  angles  and  the  other  at  the  right  end,  the  splice 


plate  should  extend  beyond  the  last 
cover-plate  splice  to  include  enough  rivets  acting  in  single  shear  to  develop 
one  plate.  It  would  be  preferable  to  splice  the  outer  plate  at  this  point 
so  that  it  would  be  in  contact  with  the  splice  plate,  but  it  is  not  customary 
to  add  an  excess  even  though  another  plate  intervenes,  as  in  the  figure, 
because  all  plates  act  together.  No  special  consideration  need  be  given 
to  the  remaining  rivets  in  the  cover  plates  because  there  will  be  an  excess 
due  to  the  fact  that  they  are  placed  opposite  those  in  the  web  legs  of  the 
angles.  Close  spacing  should  be  continued  beyond  the  inner  splice  be- 
cause an  additional  plate  begins  at  this  point  (page  274  : 1). 


276 


PART   III  — THE   DESIGN   OF   DETAILS 


1.  Illustrative  Problem  —  Field  Flange  Splice.  —  A  plate  girder  is  to 
be  spliced  in  the  field.     Each  flange  is  composed  of  2  Ls  6  X  6  X  f ,  and 
three  cover  plates  14  x  f ,  designed  at  16,000#/sq.  in.     Design  the  flange 
splice,  using  £"  rivets. 

6.94  sq.  in.  =  8.44  —  2  x  1  X  f  =  net  area  of  one  flange  angle 
5.21  sq.  in.  =  6.94  X  f  =  net  area  required  in  each  splice  angle 
5.37  sq.  in.   =  (2  X  5J  -  -^  -  2  X  l)ii  =  actual  net  area  of  lL5i  X  5£  X  H 
111,000#       =  6.94  X  16,000  =  developed  stress  of  one  flange  angle 
85,900#       =  5.37  X  16,000  =         "  "       "    "    splice     " 

41,800#       =  (111,000  -  85,900)f  =  balance  of  stress  in  opposite  splice 

angle  with  two-thirds  excess 
72,000#       =  (14  -  2  x  l)f  X  16,000  =  developed  stress  of  one  cover  plate. 

From  the  upper  table  on  page  310  the  value  of  one  field  rivet  in  single 
shear  is  6000#.  The  number  of  rivets  required  in  the  vertical  legs  of 
the  flange  angles  between  splices  is  19  =  111,000  -=-  6000.  The  total 
number  required  in  each  splice  angle  beyond  the  splice  is  15  =  85,900 
-T-  6,000,  of  which  7  =  41,800  -=-  6000  must  be  in  the  web  leg.  The  num- 
ber in  the  cover  plate  beyond  the  last  splice  is  12  =  72,000  +  6000.  The 
completed  splice  is  shown  in  Fig.  275. 

COLUMN   SPLICES 

2.  The  splices  for  mill-building  columns  are  so  simple  that  they  may 
be  designed  without  difficulty.     They  are  only  used,  as  a  rule,  where 
the  width  of  the  column  is  changed  to  accommodate  a  crane  girder  (Fig. 
135),  or  where  a  gusset  plate  replaces  part  of  the  web.     These  splices  are 
comparatively  light  and  enough  rivets  are  used  to  fully  develop  the  com- 
pressive  strength  of  the  part  spliced. 

3.  Office-building  columns  are  usually  built  in  two-story  lengths  and 
many  splices  must  be  used  in  the  larger  structures.     For  convenience  in 
erection  these  splices  are  located  just  above  the  connections  of  the  floor 
beams  and  girders.     The  heavy  cumulative  loads  make  the  use  of  milled 
ends  imperative,  and  usually  most  of  the  stress  is  transmitted  by  direct 
bearing.     When  the  full  area  of  cross  section  of  the  upper  column  bears 
upon  the  section  immediately  below  it,  splice  plates  are  used  simply  to 
hold  the  columns  in  the  proper  relative  position  and  to  transmit  the 
bending  stresses.     These  plates  are  usually  more  or  less  standardized  by 


structural  companies  for  different  types  of  columns  so  that  they  need 
not  be  designed  for  each  column.  At  some  points  in  tall  office  buildings 
it  is  necessary  to  make  a  decided  change  in  the  dimensions  so  that  only 
a  small  portion  of  the  upper  section  bears  directly  upon  the  lower  sec- 
tion, and  special  splices  must  be  designed.  Only  one  common  form 
will  be  discussed  here,  although  similar  splices  can  be  adapted  to  differ- 
ent types  of  columns. 

4.  Channel  columns  are  composed  of  two  channels  with  either  lattice 
bars  or  cover  plates  across  their  flanges,  as  shown  in  Fig.  133.  The  top 
sections  are  usually  latticed;  in  the  lower  sections,  as  the  column  loads 
increase,  the  lattice  bars  are  replaced  by  cover  plates,  and  the  plates  and 
the  channels  are  made  heavier,  until  a  point  is  reached  where  deeper 
channels  and  wider  plates  become  necessary.  Splice  plates  are  used  on 
the  flanges,  and  light  splice  angles  are  used  on  the  webs,  as  shown  at  the 
top  of  ABl  or  at  the  bottom  of  EF27,  in  the  figure  referred  to.  When 
the  channel  depth  and  plate  width  are  changed  the  conditions  are  as 
shown  in  Fig.  277  (6).  Provision  must  be  made  for  transmitting  most  of  the 
load  by  other  means  since  only  a  small  portion  of  one  column  bears  upon 
the  other.  Reinforcing  plates  are  used  to  properly  distribute  the  bear- 
ing, supplemented  by  a  \"  or  f "  bearing  plate  which  is  placed  between 
the  ends  of  the  two  columns.  The  stress  in  the  upper  cover  plates  is 
transferred  to  the  lower  cover  plates  by  reinforcing  plates  which  are 
riveted  to  the  upper  cover  plates  as  shown  in  Fig.  277  (a).  The  combined 
thickness  of  these  reinforcing  plates  or  fillers  on  each  side  of  the  column 
is  made  ^$"  less  than  the  horizontal  distance  from  the  outside  of  the 
upper  cover  plate  to  the  outside  of  the  lower  cover  plate  in  order  to  give 
a  total  clearance  of  \"  to  facilitate  the  erection  of  the  upper  column  be- 
tween the  splice  plates  which  are  riveted  to  the  lower  column.  The  rein- 
forcing plates  should  be  attached  to  the  upper  column  by  enough  rivets 
in  single  shear  to  develop  the  cover  plate.  The  field  rivets  which  con- 
nect the  splice  plate  may  be  counted  upon  to  transmit  their  full  share 
of  the  stress  from  the  cover  plate  to  the  reinforcing  plates  because  the 
two  shearing  surfaces  are  so  far  apart.  Due  attention  should  be  paid 
to  the  value  of  countersunk  rivets  (page  231 :  2)  but  usually  the  thickness 
of  the  plates  is  sufficient  to  justify  the  use  of  the  full  single-shear  value. 
The  stress  in  the  upper  channels  is  transferred  to  the  lower  channels  in 
a  similar  manner  by  reinforcing  plates  riveted  to  the  lower  channels  to 


CHAPTER   XL 


SPLICES 


277 


form  shelves.  The  combined  thickness  of  these  reinforcing  plates  on 
each  channel  is  made  from  TV"  to  f"  less  than  the  horizontal  distance  from 
the  face  of  the  upper  web  to  the  face  of  the  lower  web,  this  reduction 


Fig.  277  (a).     Channel  Column  Splice. 

being  justified  by  the  use  of  the  bearing  plate  which  distributes  the 
stresses.  The  width  of  these  reinforcing  plates  is  made  equal  to  the 
depth  of  the  upper  channel,  and  the  number  of  rivets  should  develop  the 
stress  in  this  channel.  In  developing  the  cover  plates  and  the  channels  it 
is  desirable  to  use  the  unit  stress  for  which  the  column  was  designed.  If 
this  is  not  available,  the  unit  stress  should  be  found  from  the  proper  com- 
pression formula,  substituting  the  proper  length  and  radius  of  gyration. 


Fig.  277  (6). 


When  the  formula  16,000  -  70  -  is  used  the  unit  stress  usually  ranges 

from  12,000  to  14,000. 

1.  Illustrative  Problem.  —  Channel  Column  Splice  — 
Design  a  splice  to  connect  a  "10-inch"  channel  column, 
composed  of  2-10"  LU  30#  and  2  Pis.  12  x  H,  to  a 
"  12-inch  "  column,  composed  of  2-12"  LU  30#  and 
2  Pis.  14  x  -ft-  The  distances  from  face  to  face  of  webs 
and  the  gages  are  found  from  the  table  on  page  300, 
as  recorded  in  Fig.  277  (a).  The  distance  out  to  out  of  cover  plates 
of  the  lower  column,  or  the  distance  between  splice  plates,  is  1'lf ",  so 
the  distance  out  to  out  of  reinforcing  plates  on  the  upper  column  should 
be  1'li",  in  order  to  leave  a  clearance  of  ^g"  on  each  side.  Since  the 
distance  out  to  out  of  cover  plates  is  llf ",  the  thickness  of  the  reinforc- 
ing plates  on  each  side  of  the  column  is  liV'  =  (1'li"  -  Hf ")  •*•  2, 
which  would  be  subdivided  into  \"  and  fa"  to  avoid  the  use  of 
metal  thicker  than  J"  on  account  of  punching.  The  distances  from 
back  to  back  of  webs  is  found  by  subtracting  the  web  thicknesses 
from  the  distances  out  to  out  of  webs  found  above,  and  the  thickness 
of  the  reinforcing  plates  on  each  channel  is  ff"  =  (%  x  8j  -  £) 
-  (i  X  6J  -  f£)  -  |,  which  would  be  subdivided  into  \"  and  &".  The 
least  radius  of  gyration  of  the  upper  section  may  be  found  to  be  3 . 4  (page 
21 1 : 3) ,  and  the  unsupported  length  between  floors  is  assumed  to  be 

12'0",  from  which  the  allowed  unit  stress  at  16,000  -  70  -  is  found  to  be 

about  13,000#/sq.  in.  The  developed  stress  in  one  12  X  H  plate 
is  107,300#  =  8.25  X  13,000,  and  that  in  one  10"  U  30#  is  114,700# 
=  8.82  x  13,000.  The  six  f "  field  rivets  in  single  shear  at  10,000#/sq.  in. 
are  worth  26,500#  (page  309)  and  the  number  of  shop  rivets  at  12,000#/sq. 

107,300  -  26,500 


in.  required  to  take  the  balance  is  16  = 


5300 


The  number 


required  in  the  lower  reinforcing  plates  is  22  =  114,700  -s-  5300.  Only 
two  rivets  are  used  through  the  splice  angle  so  that  it  may  be  made  simi- 
lar to  those  used  where  no  reinforcing  plates  are  necessary.  The  com- 
pleted splice  is  shown  in  the  figure. 


CHAPTER  XLI 


PINS 

SYNOPSIS:  A  single  cylindrical  pin  may  be  used  instead  of  rivets  to  connect  different 
members  at  a  joint.  Such  a  pin  is  designed  as  a  beam,  but  the  forces  do  not,  as  a  rule, 
lie  in  the  same  plane. 


1.  Description.  —  The  joints  of  bridge  trusses  may  be  either  riveted 
or  pin-connected,  as  explained  on  page  121  : 1.  Only  one  pin  is  used  at  a 
joint  in  a  pin-connected  truss  and  greater  flexibility  is  thus  obtained 
than  in  a  truss  with  fully  riveted  joints,  because  the  members  are  free 
to  turn  upon  the  pin  as  the  truss  deflects,  without  causing  secondary 
stresses.  Similar  small  pins  are  used  in  conjunction  with  loop-rods, 
U-bolts,  and  clevises.  These  small  pins  may  be  simply  rough  or  turned 
bolts  with  ordinary  heads  and  nuts,  or  they  may  be  "cotter  pins"  either 


Fig.  278  (a). 


Fig.  278  (6). 


with  a  special  head  at  one  end  and  a  hole  for  a  "cotter"  at  the  other 
(Fig.  279)  or  with  cotters  at  both  ends.  The  larger  bridge  pins  are  turned 
cylinders  with  threaded  ends  of  reduced  diameter  upon  which  pilot  nuts 
and  driving  nuts  (Fig.  278  (a))  are  screwed  for  use  in  erection.  These  pins 
are  driven  cold  without  upsetting,  the  holes  in  the  members  being  from 
wi"  to  ^"  larger  than  the  diameters  of  the  pins.  The  pins  are  held  in 
position  by  recessed  nuts  called  "Lomas  nut"  or  nuts  with  washers 
(Fig.  278  (b))  which  replace  the  temporary  driving  and  pilot  nuts.  Pins 
over  10"  in  diameter  may  have  caps  instead  of  nuts,  held  in  place  by 
small  rods  passed  through  holes  in  the  pins. 


2.  Pins  are  designed  as  cylindrical  beams  to  resist  both  bending 
shear.     Usually  the  size  of  the  pin  will  be  determined  by  the  bending 
moment,  but  the  strength  of  the  resulting  cross  section  should  be  in- 
vestigated for  it  may  be  necessary  to  increase  the  size  of  the  pin  as  a 
result.     Each  member  which  bears   upon  a  pin  must    furnish   sufficient 
bearing  area  to  properly  distribute  the  stress  in  that  nember.     This  bear- 
ing area  is  the  product  of  the  diameter  of  the  pin  by  the  thickness  of  the 
metal  which  bears  upon  the  pin  (compare  page  230  :  3).     The  bearing  area 
of  riveted  members  may  be  increased  by  the  use  of  reinforcing  plates, 
as  explained  in  the  next  chapter  (page  284),  but  when  this  is  not  feasible 
the  minimum  diameter  of  the  pin  may  be  determined  by  the  bearing  in 
some  member.     Thus  the  minimum  diameter  of  pin  used  in  any  eye 
bar  may  be  found  by  dividing  the  total  stress  in  the  bar  by  the  thick- 
ness of  the  bar  and  by  the  unit  stress  in  bearing.     Often  a  minimum 
of  5"  or  eight-tenths  of  the  width  of  the  eye  bar  is  specified  for  bridge 
work. 

3.  Application  of  Forces.  —  For  convenience  in  finding  the  bending 
moment  on  a  pin  it  is  usually  assumed  that  the  force  due  to  the  stress 
on  a  member  or  part  of  a  member  acts  upon  the  pin  as  if  concentrated 
at  the  center  of  bearing,  i.e.,  the  center  of  the  surface  of  contact.     This 
assumption  is  on  the  side  of  safety,  and  the  slight  increase  in  the  size 
of  the  pin  is  relatively  unimportant.     The  bearing  may  depend  not  only 
upon  the  thickness  of  the  main  part  of  a  member,  but  also  upon  the  thick- 
ness of  any  reinforcing  plates  which  may  be  needed  (see  above).    Since 


278 


CHAPTER   XLI 


PINS 


279 


the  bearing  depends  upon  the  diameter  of  the  pin,  the  two  are  interde- 
pendent and  either  the  thickness  or  the  diameter  must  be  first  assumed 
and  later  verified.  In  this  chapter  the  plate  thickness  is  assumed  to  be 
correct.  In  the  case  of  a  small  pin  for  a  clevis  or  a  loop-rod,  all  forces 
lie  in  the  same  plane,  and  the  bending  moment  is  found  as  in  a  simple 
beam.  At  a  joint  in  a  bridge  truss,  however,  the  forces  are  not  con- 
fined to  a  single  plane,  and  the  position  of  the  point  of  maximum  bending 
moment  is  not  so  apparent. 

1.  Design  for  Bending.  — As  in  the  design  of  other  beams,  the  maxi- 
mum bending  moment  is  equated  to  the  resisting  moment.     For  a  beam 
of  circular  cross  section  the  resisting  moment  is  0.098/d3,  where  /  is  the 
unit  stress  in  bending  and  d  the  diameter  (page  200:1).     The  unit  stress, 
in  bending  is  usually  about  50%  greater  than  for  other  beams,  24,000#/sq. 
in.  being  specified  by  the  American   Railway  Engineering  Association. 
In  order  to  facilitate  the  designing  of  pins,  a  table  of  resisting  moments 
for  different  values  of  /  and  d  is  shown  on  page  333. 

2.  Investigation  for  Shear.  —  In  determining  whether  a  pin  designed 
for  bending  has  sufficient  area  to  resist  the  shear,  it  should  be  remem- 
bered that  the  intensity  of  the  shearing  stress  is  not  uniform  throughout 
the  cross  section,  but  is  greatest  at  the  neutral  axis.     The  maximum  shear 

4V       16F 

intensity  is  four-thirds  the  average  intensity,  or  — -^  =  5—™,  where  V  is 


16  x  8  000 
tensity  is  6000#/sq.   in.  =  -5  —  ,\>,  ,  which  is  safely  under  the  10,000 


ee    i 


the  maximum  shear,  r  and  d  the  radius  and  the  diameter,  respectively, 
of  the  pin  (page  202  :  1).  This  maximum  shear  intensity  must  not  exceed 
the  allowed  unit  stress  hi  shear,  which  is  usually  the  same  as  for  shop 
rivets  and  usually  one-half  the  unit  stress  in  bending  or  bearing. 

3.   Illustrative  Problem.  —  Co-planar  Forces.      Design  a  phi  to  fasten 
a  1"  square  loop-rod  between  two  \"  plates,  as  shown  in  Fig.  279.     The 

stress  in  the  rod  is  16,000#,  and  the 
stress  in  each  plate  is  one-half  this 
amount.  The  distance  from  the  center 
of  bearing  of  the  rod  to  the  center  of 

bearing  of  one  plate  is  f"  =  J(l  +  5),  and  the  maximum  bending  mo- 
ment on  the  pin  at  the  center  is  6000#in.  =  8000  X  f  .  Using  a  unit 
stress  in  bending  of  20,000#/sq.  in.,  the  required  diameter  of  the  pin  may 
be  found  from  the  table  on  page  333  to  be  1J".  The  maximum  shear  in- 


=. 


allowed. 

4.  Not  every  pin  in  a  truss  need  be  designed  because  it  is  impractical 
to  use  so  many  different  sizes.     It  is  preferable  to  make  several  phis  alike 
in  order  to  reduce  the  number  of  different  eye  bars  to  be  made  and  the 
number  of  different  pin  holes  to  be  bored.     It  is  customary  to  calculate 
the  size  of  the  pins  at  the  shoe  (Fig.  290),  at  the  hip,  at  the  top-chord 
joint  next  to  the  hip,  and  at  the  bottom-chord  joint  nearest  the  center. 
Except  for  very  long  spans,  the  remaining  pins  in  the  bottom  chord  may 
be  made  like  the  central  pin,  and  .the  remaining  top-chord  phis  may  be 
made  like  that  in  the  joint  next  to  the  hip.     Often  the  lower  pins  can  be 
made  like  the  upper  ones. 

5.  The  arrangement  of  the  different  members  on  a  pin  has  its  effect 
upon  the  size  required.     The  arrangement  is  usually  termed  the  "pack- 
ing."    Sometimes  the   results  of  two  or  more   different  arrangements 
must  be  compared  in  order  that  the  best  one  may  be  selected.     The 
packing  on  a  pin  is  made  symmetrical,  and  therefore  members  which  are 
composed  of  eye  bars  should  have  an  even  number  of  bars,  and  riveted 
chord  members  and  posts  should  have  two  or  more  webs.     A  single  stir- 
rup or  small  counter  is  sometimes  placed  at  the  center.    The  bars  of  diag- 
onals are  usually  placed  next  to  the  posts  in  order  to  reduce  the  bending 
moments.     No  two  eye  bars  of  a  single  member  should  be  placed  in  con- 
tact as  it  would  be  impossible  to  paint  between  them.     Unless  a  bar  of 
an  opposing  member  is  placed  between  two  bars  of  one  member,  the 
latter  should  be  separated  on  the  pin  by  a  collar  at  least  1"  wide.     The 
pin  is   thus  lengthened   2",  but  the  diameter  may  often   be   reduced 
considerably.     Unless  the  bars  on  a  pin  are  within  \"  of  each  other,  the 
space  between  them  should  be  filled  with  a  washer  or  collar  in  order  to 
maintain  the  proper  spacing  of  the  bars  in  accord  with  the  design.     In 
determining  the  distances  from  center  to  center  of  bearings  used  in  com- 
puting the  bending  moments,  an  allowance  of  at  least  TV"  should  be  made 
between  adjacent  bars  to  allow  for  paint,  for  scale,  and  for  variation  in 
thickness.     A  clearance  of  J"  should  be  left  between  the  bars  and  the 
built  members,  due  allowance  being  made  for  the  heads  of  rivets  in  rein- 
forcing plates  or  other  component  parts.     It  is  often  necessary  to  flatten 


280 


PART  III  — THE   DESIGN  OF  DETAILS 


or  countersink  these  rivets.  The  flanges  of  channels  or  angles  are  often 
notched  to  clear  the  bars,  provided  the  webs  are  properly  reinforced. 
The  packing  at  one  pin  is  dependent  upon  that  at  the  adjacent  pins  be- 
cause the  bars  should  be  kept  approximately  parallel.  A  bar  should  not 
slope  more  than  -fa"  per  foot.  If  it  is  necessary  to  use  a  greater  slope 
the  bars  should  be  bent  to  furnish  better  bearing  on  the  pins. 

1.  Since  the  forces  which  act  upon  a  pin  in  a  truss  do  not  lie  in  the 
same  plane,  each  force  should  be  resolved  into  horizontal  and  vertical 
components.     The  position  of  the  point  of  maximum  bending  moment 
is  usually  not  apparent,  so  it  becomes  necessary  to  find  the  bending  mo- 
ment due  to  the  horizontal  components,  and  that  due  to  the  vertical 
components    at   each    point    of    concentration.     The    resultant    bending 
moment  at  each  point  will  be  the  square  root  of  the  sum  of  the  squares 
of  the  horizontal  and  the  vertical  bending  moments  at  that  point.     Care 
must  be  taken  not  to  combine  the  horizontal  bending  moment  at  one  point 
with  the  vertical  bending  moment  at  another.     The  maximum  bending 
moment  on  a  pin  will  often  occur  at  a  point  where  there  is  no  vertical 
bending  moment.     The  use  of  the.  table  of  squares  on  page  332,  or  the 
diagram  on  page  312,  is  recommended  in  finding  the  resultants. 

2.  The  forces  which  act  upon  a  pin  must  be  selected  with  great  care. 
The  values  on  the  stress  diagram  show  the  maximum  stresses  for  which 
each  complete  member  is  designed,  but  these  maximum  stresses  do  not 
occur  in  all  members  of  a  truss  simultaneously.     The  maximum  chord 
stresses  are  found  when  the  truss  is  fully  loaded,  but  the  maximum  web- 
member  stresses  are  found  when  the  truss  is  only  partially  loaded.     Care 
should  be  taken  to  use  either  the  maximum  chord  stresses  and  the  cor- 
responding stresses  in  the  web  members,  or  conversely,  the  maximum 
stresses  in  the  web  members  and  the  corresponding  chord  stresses.     As 
a  rule,  the  first  condition  will  govern  the  size  of  the  pin  at  the  shoe  and 
at  the  hip,  the  second  condition  will  govern  the  size  of  the  remaining 
top-chord  pins,  but  either  condition  may  govern  the  size  of  the  bottom- 
chord   pins.     Counters  are  not  stressed  when  the  main  diagonals  are 
stressed,  but  they  must  be  considered  in  packing  the  pin  because  they 
will  cause  increased  lever  arms  which  will  affect  the  bending  moments. 
The  stresses  which  act  upon  a  pin  at  any  one  time  must  be  in  equilibrium. 
To  insure  this,  only  the  maximum  chord  stresses  or  the  maximum  stresses 


in  the  diagonals  should  be  taken  from  the  stress  diagram,  and  the  other 
stresses  should  be  computed  to  correspond.  It  is  well  not  to  use  the 
stress  in  a  post  as  given  on  the  diagram  because  the  stress  on  the  pin 
may  differ  on  account  of  the  method  of  supporting  the  floor  beam.  In 
a  bottom-chord  joint  governed  by  maximum  chord  stresses,  these  chord 
stresses  are  taken  from  the  diagram  and  divided  proportionately  among 
the  component  parts  of  the  members.  A  sketch  is  drawn  showing  all  of 
these  horizontal  forces  and  the  horizontal  components  of  the  forces  in 
the  component  parts  of  the  diagonals.  The  proper  magnitudes  of  the 
latter  forces  may  be  determined  from  the  H  equation  of  equilibrium. 
The  vertical  components  may  be  determined  from  these  horizontal  com- 
ponents, and  the  corresponding  forces  in  the  component  parts  of  the  post 
may  be  found  from  the  V  equation.  Similarly,  in  a  top-chord  joint  the 
maximum  stress  in  the  diagonal  is  taken  from  the  diagram,  and  the 
corresponding  stresses  in  the  other  members  are  computed.  In  case  the 
adjacent  top-chord  members  are  in  the  same  straight  line,  only  the  differ- 
ence in  their  stresses  need  be  found,  since  the  members  bear  on  opposite 
sides  of  the  pin  and  cause  no  bending. 

3.  Computation.  —  Since  the  forces  on  a  pin  are  symmetrically  placed, 
it  is  necessary  to  determine  the  bending  moments  on  only  one-half  of  the 
pin,  care  being  taken  to  count  only  one-half  of  a  force  at  the  center.     The 
bending  moment  at  one  point  may  be  best  found  from  the  bending  mo- 
ment at  the  preceding  point  by  adding  algebraically  the  product  of  the 
shear  for  a  section  between  the  points  by  the  distance  between  the  points 
(page  189:1).     It  is  convenient  to  arrange  the  computation  in  tabular 
form  as  shown  in  the  problems  which  follow.     When  finding  the  result- 
ant bending  moment  from  the  two  components  it  should  be  remembered 
that  the  horizontal  bending  moment  is  constant  between  the  horizontal 
force  nearest  the  center  and  the  corresponding  force  on  the  opposite  side 
of  the  center.     This  should  be  obvious  because  the  shear  is  zero.     The 
actual  position  of  the  bars  on  a  pin  may  vary  slightly  from  the  spacing 
used  in  the  design,  and  it  is  therefore  consistant  to  use  lever  arms  to  the 
nearest  |",  and  shears  and  bending  moments  to  the  nearest  thousand 
pounds  or  pound-inches. 

4.  Illustrative  Problem.  —  Bottom-chord  Pin.     Design  the  pin  at  the 
joint  L3  of  the  truss  shown  in  Fig.  281  (a).     Let  us  assume  that  the  size  of 


CHAPTER   XLI 


PINS 


281 


the  pin  will  be  determined  when  the  chord  stresses  are  maximum,  and 
that  the  arrangement  of  the  bars  can  be  selected  without  regard  to  the 
other  joints  of  the  truss.  Let  us  assume  also  that  the  reinforcing  plates 


First  Arrangement 


113 


4  tiara  S\  I%"L3  4  bars  8"x  I<J"  L4 
7 panels  ®  28Le"=l99'-6" 


Fig.  281  (a). 

on  the  post  have  been  determined  from  an  assumed  size  of  pin,  and  that 
the  resulting  size  is  the  same  as  assumed.  The  results  of  the  two  ar- 
rangements shown  in  the  figures  will  be  compared.  In  both  arrange- 
ments the  bars  of  the  main  diagonal  are  placed  next  to  the  post,  and  the 
counters  between  the  diagonals  and  the  chord  bars.  Inclined  bars  may 
be  differentiated  from  the  horizontal  bars  by  section  lines  as  shown. 
The  smaller  chord  bar  is  placed  at  the  end,  and  the  other  chord  bars  are 
alternated  in  the  first  arrangement,  or  placed  as  shown  in  the  second 
arrangement  with  a  1"  collar  between  the  two  larger  bars.  The  stress 
in  thousands  of  pounds  in  each  of  the  four  8  X  lf£  bars  is  217  =  868  -s-  4, 
and  in  each  of  the  8  x  Iff  bars  is  247  =  986  -=-  4.  In  order  to  satisfy 
the  H  equation,  the  horizontal  component  in  the  main  diagonal  must  be 
60  =  2  x  247  —  2  x  217.  The  corresponding  vertical  component  is 

34  0 

71  =  60  X  ^T-?,  and  the  force  in  one-half  the  post  must  be  the  same, 
/o .  o 

These  forces  are  shown  in  the  small  sketches,  together  with  the  lever 
arms  which  are  found  as  follows: 


2f"  =  iUtf  +  li)  +  IA  +  2  x  A 

l?"  =  i(l?+l+  A)  +  i  ^he  rivets  being  countersunk) 
3"  =  111  +  1  +  A 


<  /—  ! 

1 

Z^s'i'H 

A  /H") 

1 

(  s*'n 

fcjy  ff",  t  '  " 

8*1^'  mm 

1 

sCen'er  line. 

217  f  — 

0. 

T 

^.247 

~M» 

^/7<  

2~~ 

3 

^.247 

60"  — 

4*> 

71  *  

\4 

—  T 

^r 

1 

Z-^71 





Fi 

g.  281  (i 

). 



Horizontal  Components 

Vertical  Components 

Shear 

Lever 
Arm 

Product 

Bending 
Moment 

Point 
of 
Moments 

Shear 

Lever 
Arm 

Product 

Bending 
Moment 

1000i« 

In. 

lOOOf  in. 

lOOOf  in. 

1000# 

In. 

lOOOifin. 

1000#in. 

-217 

11 

-407 

-407 

1 

+  30 

li 

+56 

-351 

2 

-187 

U 

-351 

-702 

3 

+  60 

2| 

+165 

-537 

4 

0 

-537 

5 

-71 

U 

-89 

-89 

The  maximum  bending  moment  for  this  arrangement  is  702  at  point  3, 
since  this  is  obviously  greater  than  the  resultant  "V/5372  +  S92  at  point  5. 
It  is  unnecessary  to  carry  the  solution  further  until  the  results  of  the 
second  arrangement  are  obtained. 


282 


THE   DESIGN   OF  DETAILS 


Second  Arrangement 

i'r     i  i 


ri/J 


"Collar^ 

\              \                                                           l 

!       !                              i 

\              \ 

—  4"  i  .—  1—  J"' 

217-*—. 
I 


2171 

eo-> 


Center  Line, 


^+•247 


* 


Fig.  282(o). 


Horizontal  Components 

Vertical  Components 

Shear 

Lever 
Arm 

Product 

Bending 
Moment 

Point 
of 
Moments 

Shear 

Lever 

Arm 

Product 

Bending 
Moment 

lOOOf 

In. 

lOW  in. 

1000#  in. 

10001 

In. 

HXXW  in. 

1000#in. 

-217 

H 

-407 

-407 

1 

+  30 

3 

+  90 

-317 

2 

+277 

11 

+519 

+202 

3 

+  60 

2| 

+165 

+367 

4 

0 

+367 

5 

-71 

U 

-89 

-89 

16  X  277,000 


This  is  less  than  the  diameter  required  to  sati 


3  *  12,000 

the  bending  moment  of  the  first  arrangement  and  hence  is  used.    In  neither 
arrangement  does  the  presence  of  the  counter  increase  the  size  of  the  pin. 
If  the  maximum  bending  moment  was  found  at  point  4  or  5,  it  might  be  de- 
sirable to  place  the  counters  between  the  channels  of  the  post,  cutting  the 
flanges  if  necessary,  in  order  to  reduce  the  lever  arm  between  points  3  and  4. 
1.  Illustrative  Problem.  —  Pin  at  Hip.      Design  the  pin  at  the  joint 
Ul  of  the  truss  shown  in  Fig.  281  (a).     Let  us  assume  that  the  reinforcing 
plates  on  the  members  which  meet  at  this  point  have  been  designed  from 
an  assumed  diameter 

Of  pin  Which  proves  tO      '    "^ffif""^.       r     ~T      T     1        '  [  /Center  of  betting  UI-2 

be  correct,   and   that 

the    arrangement    on 

the  pin  is  as  shown  in 

Fig.     282  (6).       The 

outer  reinforcing  plate 

of  the  top  chord  and 

the  inner  plate  of  the 

end  post  are  extended 

to  hold  the  pin  in  position  against  shock  and  to  protect  the  joint  from 

the  weather.     The  centers  of  bearing  of  these  two  mem  ers  are  therefore 

not  quite  opposite.     The  diagonal  is  placed  between  the  end  post  and 

the  hip  vertical  with  ample  clearance  for  countersunk  rivets  in  each  so 

the  rivets  need  not  be  chipped.     As  a  rule  only  the  full  load  which  causes 

maximum  stresses  in  the  end  post,  the  top  chord,  and  the  hip  vertical 

need  be  considered.     From  the  panel  lengths  and  depths  the  lengths  of 

the  members  may  be  calculated,  and  the  components  of  the  maximum 


Fig.  282(6). 


Vertical  Components 


The  maximum  bending  moment  for  this  arrangement  is  407  at  point  1,      stresses  in  these  members  may  be  found  by  proportion,  thus: 
since  this  is  more  than  the  resultant  V3672  +  892  at  point  5.     This  ar- 
rangement gives  a  smaller  bending  moment  and  is  therefore  adopted. 
Using  a  unit  stress  in  bending  of  24,000#/sq.  in.,  we  find  from  the  table 
on  page  333  that  a  5|"  pin  is  required  for  a  bending  moment  of  407,000# 

16  x  277  000 
in.     The  maximum  intensity  of  shear  is  14,200  =  — 5 — 7^3^ — 


Horizontal  Components 
oo  e: 

EP  =  606  =  881  x  T 

41.4 


EP  =  638  =  881  X 


exceeds  the  allowed  value  12,000,  so  the  diameter  must  be  increased  to 


Ul-2  =  866 
LI  Ul  =  0 


877  x 


28.5 
28.8 


£71-2  =  120  =  877  X 
LI  Ul  =  244 


30.0 

41.4 

4.0 

28.8 


CHAPTER   XLI 


PINS 


283 


Since  each  of  these  members  bears  upon  the  pin  at  two  points  of  con- 
centration the  above  values  should  be  divided  by  2,  and  recorded 
on  the  sketch  as  shown.  The  corresponding  components  in  each  bar 
of  the  diagonal  L2  Ul  may  be  found  from  the  H  and  V  equations  of 
equilibrium. 

From  the  bending  moments  tabulated  on  this  page  the  maximum  bend- 
ing moment  is  found  to  be  1154  =  V7202  +  9022  at  point  3.  At  24,000# 
/sq.  in.  this  requires  an  8"  pin.  The  maximum  shear  is  437  =  V4332  +  602, 

16  x  437,000 


and  the  maximum  shear  intensity  is  11,600#  = 
than  the  allowed  12,000. 


37T82 


which  is  less 


303- 


SO- 


Fig.  283. 


'319 
^137 
>I22 


Horizontal  Components 

Point 
of 
Moments 

Vertical  Components 

Shear 

Lever 
Arm 

Product 

Bending 
Moment 

Shear 

Lever 

Arm 

Product 

Bending 
Moment 

lOW 

In. 

100W  in. 

1000*  in. 

1000# 

In. 

1000(1  in. 

ll*)0.  in. 

-433 
-130 
0 

I 

2! 

-379 
-341 

-379 
-720 
-720 

1 

2 
3 

+60 
-259 
-122 

2J 

2* 

+53 

-680 
-275 

+53 
-627 
-902 

CHAPTER   XLII 
REINFORCING  PLATES 

x  SYNOPSIS:  The  webs  of  riveted  members  of  pin-connected  trusses  must  be  reinforced 
at  the  ends  in  order  that  they  may  properly  transmit  the  stresses  to  the  pins.  The 
method  of  designing  reinforcing  plates  is  here  shown. 


1.  When  Used.  —  Reinforcing  plates  are  used  to  strengthen  the  weaker 
parts  of  members  in  order  to  fully  develop  the  strength  of  the  remaining 
parts.     Usually 'such  reinforcement  occurs  at  the  ends  of  the  members. 
Reinforcing  plates  are  used  on  girder  webs  (page  266:  3),  at  the  splices  of 
certain  office-building  columns  (page  276:4),  at  the  joints  of  pin-connected 
trusses,  and  at  similar  places.     The  method  of  designing  the  reinforcing 
plates  of  pin-connected  riveted  members  is  illustrated  in  this  chapter- 
These  plates  are  often  termed  "pin  plates"  and  their  design  typifies  the 
design  of  all  reinforcing  plates. 

2.  Type  of  Member.  —  A  compression  member  in  the  chord  of  a  simple 
pin-connected  truss  is  usually  composed  of  two  channels  with  one  cover 
plate  (Fig.  122),  or  of  two  or  more  web  plates  with  angles  and  one  or 
more  top  cover  plates  (Fig.  128).     A  compression  web  member  is  often 
composed  of  two  channels.     Each  end  of  these  members  bears  against  a 
cylindrical  pin  which  is  located  at  or  near  the  center  lines  of  the  webs. 
Since  no  other  part  of  the  member  bears  against  the  pin  the  whole  stress 
must  reach  the  pin  through  the  webs,  which  must  be  reinforced  to  fur- 
nish the  necessary  bearing.     Most  of  the  tension  members  of  a  pin-con- 
nected truss  are  composed  of  eye  bars  and  these  need  no  reinforcement. 
A  riveted  tension  member  is  often  used  in  the  two  end  panels  of  the  bot- 
tom chord  to  provide  for  a  reversal  of  stress. 

3.  Method  of  Design.  —  All  reinforcing  plates  must  be  designed"  to 
furnish  the  necessary  bearing  area  for  the  pin.     This  part  of  the  design 
consists  in  finding  the  thickness  of  the  plates  and  the  number  of  rivets 


required  to  fasten  them  to  the  webs.  The  width  of  the  plates  are  usually 
made  as  large  as  the  available  space  will  accommodate,  and  the  length 
depends  upon  the  number  and  the  spacing  of  the  rivets.  The  size  of  the 
pin  must  either  be  predetermined  or  assumed  (see  page  278: 2).  The  rein- 
forcing plates  for  a  pin-connected  tension  member  composed  of  channels 
or  plates  and  angles  must  not  only  provide  the  proper  bearing,  but  also 
the  necessary  net  section.  To  prevent  failure  at  the  pin,  the  net  section 
through  the  pin  hole  must  exceed  the  net  area  for  which  the  main  mem- 
ber is  designed.  The  amount  of  this  excess  is  usually  specified  as  25%. 
The  location  of  the  rivets  in  the  reinforcing  plates  of  a  tension  member 
must  receive  special  consideration.  Provision  must  be  made  to  properly 
reinforce  a  member  which  is  weakened  by  having  part  of  the  flanges  cut 
away  for  clearance. 

4.  Design  for  Bearing.  —  One-half  the  total  stress  in  a  member  with 
two  webs  is  imparted  to  the  pin  through  each  web  and  its  reinforcing 
plates.  When  there  are  more  than  two  webs,  the  proportion  will  be 
approximately  equal  to  the  relative  cross-sectional  areas  included  be- 
tween lines  drawn  midway  between  the  webs.  The  bearing  area  of  each 
web  and  its  reinforcing  plates  is  found  by  dividing  the  corresponding 
stress  (one-half  or  other  portion  of  the  total  stress)  by  the  unit  stress 
allowed  for  bearing.  The  combined  thickness  of  the  web  and  its  rein- 
forcing plates  is  found  by  dividing  this  area  by  the  diameter  of  the  pin 
(compare  bearing  on  rivets,  page  230:3).  The  web  thickness  is  deducted 
from  this  combined  thickness,  leaving  the  required  thickness  of  the  rein- 


284 


CHAPTER   XLII 


REINFORCING  PLATES 


285 


forcing  plates,  which  should  be  increased  to  the  nearest  commercial  size 
(a  multiple  of  -jV')-  The  total  thickness  may  be  subdivided  into  as  many 
parts  as  are  best  suited  to  particular  conditions.  It  is  usually  desirable  to 
place  part  of  the  plates  on  each  side  of  the  web  to  make  the  rivets  more 
effective.  No  single  plate  should  exceed  \"  on  account  of  punching. 

1.  The  number  of  rivets  in  the  reinforcing  plates  should  fully  develop 
the  plates.  If  the  plates  are  all  on  one  side  of  the  web,  the  rivets  act 
in  single  shear,  but  if  part  of  the  plates  are  on  each  side,  the  rivets  act 
in  double  shear.  The  limiting  value  of  each  rivet  must  be  selected  with 
care  because  often  the  bearing  value  in  a  channel  web  is  less  than  the 
single-shear  value,  or  the  bearing  value  in  a  heavy  web  is  more  than  the 
double-shear  value.  For  the  value  of  countersunk  or  flattened  rivets, 
see  page  231 : 2.  The  bearing  value  in  webs  which  are  not  multiples  of  ^" 
may  be  found  by  multiplying  the  decimal  thickness  by  the  rivet  diameter 
and  by  the  unit  stress  in  bearing.  This  should  be  necessary  only  when 
the  number  of  rivets  is  large;  it  is  usually  close  enough  to  roughly  inter- 
polate a  value  from  the  tables,  or  to  use  a  value  given  for  the  nearest  -rs", 
preference  being  given  to  the  lower  of  two  values.  The  developed  stress 
in  the  plates  is  the  product  of  the  total  thickness  of  the  reinforcing  plates 
by  the  diameter  of  the  pin  and  by  the  unit  stress  in  bearing.  This  value 
should  be  used  to  find  the  total  number  of  rivets  when  the  plates  are  all 
on  one  side  of  the  web  or  when  the  plates  are  about  equally  divided  on 
opposite  sides.  The  rivets  should  distribute  the  stress  proportionately 
among  the  component  parts  of  the  member  as  far  as  practicable.  Thus 
enough  rivets  should  connect  the  reinforcing  plates  to  the  bottom  angle 
to  develop  the  stress  in  the  angle,  and  rivets  in  the  top  angle  should 
develop  the  angle  and  part  of  the  cover  plate.*  See  Fig.  128.  When 
more  than  one  plate  is  used  on  the  same  side  of  the  web,  or  when  the 
plates  on  opposite  sides  differ  considerably  in  thickness,  the  plates 
may  be  made  of  different  lengths  because  it  is  unnecessary  that  they 
contain  the  same  number  of  rivets.  The  stress  in  each  plate  is  propor- 
tional to  its  thickness  and  equal  to  the  product  of  the  thickness  by  the 
diameter  of  the  pin  and  by  the  unit  stress  in  bearing.  The  plates  on 
opposite  sides  of  the  web  may  be  considered  separately.  There  must 

*  For  illustrative  problems  see  Johnson-Bryan-Turneaure's  "Modern  Framed 
Structures,"  Part  III,  John  Wiley  and  Sons,  Inc.,  New  York. 


be  enough  rivets  through  the  outer  plate  to  develop  that  plate,  there 
must  be  sufficient  rivets  through  the  two  outer  plates  to  develop  both 
plates,  and  so  on,  the  number  in  the  plate  next  to  the  web  being  deter- 
mined by  the  stress  in  all  the  plates  on  that  side  of  the  web.  The  rivets 
do  not  all  have  the  same  limiting  value,  however.  Those  which  pass 
through  plates  on  only  one  side  of  the  web  may  be  counted  in  single  shear, 
unless  the  bearing  value  in  a  channel  web  is  less.  One-half  the  value  of 
the  rivets  which  pass  through  plates  on  both  sides  of  the  web  may  be 
counted  in  developing  the  plates  on  each  side.  This  will  be  one-half  * 
the  bearing  value  unless  the  thickness  of  the  web,  or  the  web  and  the 
angles  through  which  part  of  the  rivets  may  pass,  is  great  enough  to 
develop  double  shear,  in  which  case  the  half  value  equals  the  single-shear 
value.  The  thicker  plate  should  be  placed  next  to  the  web.  Each  plate 
is  cut  at  right  angles  to  the  axis  of  the  member.  The  length  of  each  plate 
should  be  as  great  as  the  width,  or  at  least  three-quarters  of  the  width, 
in  order  to  fully  develop  the  rivets  near  the  edges.  In  bridges  it  is  cus- 
tomary to  let  a  thin  outer  plate  extend  around  the  pin,  as  in  Fig.  127, 
in  order  to  cover  the  joint  between  members  and  to  hold  the  members 
hi  position  during  erection.  Rivets  in  tension  members,  and  in  com- 
pression members  where  the  pin  is  not  at  the  extreme  end,  should  meet 
the  added  requirements  of  page  286:2. 

2.  Illustrative  Problem.  —  Compression  Member.  Design  the  rein- 
forcing plates  at  the  end  of  a  compression  member  composed  of  two 
12"  LiJ  30#  and  one  cover  plate  14  x  f .  The  maximum  stress  in  the 
whole  member  is  342,000#.  Use  a  4"  pin  and  f "  rivets,  with  a  unit  stress 
in  bearing  of  24,000#/sq.  in. 

171,000#  =  342,000  +  2  =  stress  hi  each  web  and  its  reinforcement 
171,000 


1.78"  = 


=  combined  thickness  of  web  and  plates 


4  X  24,000 
1^"  =  1-27"  =  1.78  -  0.51=  thickness  of  reinforcing  plates 

126,000#  =  Ifk  X  4  X  24,000  =  developed  stress  in  plates. 
Part  of  the  plates  should  be  placed  on  each  side  of  the  web,  preferably, 
the  inner  ones  extending  the  full  depth  of  the  channel,  the  outer  ones 
*  More  strictly,  the  bearing  value  is  divided  in  proportion  to  the  relative  thickness 
of  the  plates  on  the  opposite  sides  of  the  web,  but  this  is  usually  not  necessary,  and  it 
is  not  consistent  with  the  usual  method  of  designing  riveted  joints. 


286 


THE   DESIGN   OF  DETAILS 


being  limited  to  10"  to  clear  the  flanges.  If  the  plates  are  about 
equally  divided,  as  shown  in  Fig.  286  (a),  the  rivets  are  limited 
by  the  bearing  in  the  \"  channel  web,  and  the  total  number  required  is 

14  =  126,000  -=-  9000.      If 


9    " 

T¥ 


[o  o  o  o  o 

J  O  O  O  O 

o  o  o  o  o 

2-12"&  30*  I 

2  Pls.io'xj'*  I'-s") 
2  P/S./2"  ll'i  lla 

Fig.  286  (a). 

where  on  only  one  side. 

|  X  4  x  24,000 
- 


is   o 


4500 

X  4  x  24,000 
4500 


:  plate  is  used  on  the  inside  and 
two  f"  plates  on  the  outside,  as 
shown  in  Fig.  286  (b),  the  rivet 

i  value  counted  on  each  side  of  the 

web  is  4500  =  9000  -r-  2  where 
plates  are  on  both  sides,  and  5300 

The  number  required  in  the  outer  |"  plate 

The   number  required   in  the   TV  plate   is   12 


„, 

Ihese  12  rivets  provide  also  for  an  equal  stress  in 


the  two  |"  plates  so  that  the  additional  number  in  single  shear  is  4 

(f  -  A)  4  X  24,000 

=  —  -    conr>  --     bince  12  rivets  cannot  be  arranged  to  advantage 
ooUU 

14  are  used  in  the  A"  plate.     By  this  arrangement  it  is  unnecessary  to 

use  16  =  12  +  4  rivets  in  the  other  f  " 

plate  because  by  extending  the  inner 

plate  all  rivets  pass  through  plates  on 

both  sides,    and    14    in    bearing    are 

sufficient  for  the  total  stress,  as  found 

above  for  two  plates. 

1.  Design  for  Tension.  —  The  rein- 
forcing plates  of  pin-connected  tension 
members  are  designed  for  bearing,  as 
on  page  284:  4,  but  they  must  also 
satisfy  another  requirement.  The  pin 
tends  to  tear  out  toward  the  end  of 


'0 

0 

o 

o 

0 

2-l2"<2 

30*         \ 

^J 

o 

o 

0 

0 

]? 

pis.id'xi 

x 

l'-3"          . 

!  o 

0 

Q. 

o 

0 

-J2 

Pls.l2"x£ 

* 

l'-3"         I 

2  Pls.io'xj  x  l'-2" 


1 

O  O   O  i  'Ox                      / 

N\/l 

t"       —  J 

0  O  O 

xoy  i 

Fig.  286  (6). 


the  member,  and  unlike  a  compression  member  the  whole  bearing  is 
on  the  outer  half  of  the  pin.  As  far  as  bearing  is  concerned  the  rein- 
forcing plates  could  be  placed  entirely  beyond  the  pin,  where  they 
would  act  as  in  a  compression  member,  but  the  strength  of  the  main 
member  at  the  pin  would  not  be  sufficient  to  transmit  the  stress.  This 


part  of  the  member  must  be  reinforced,  and  logically  the  same  reinforc- 
ing plates  are  extended  for  this  purpose.  The  plates  should  be  made 
thick  enough  for  tension  as  well  as  for  bearing.  According  to  a  common 
clause  in  the  specifications,  the  total  net  area  of  cross  section  through 
the  pin  hole  of  a  tension  member  must  exceed  by  at  least  25%  the  net 
area  for  which  the  main  member  is  designed.  The  latter  net  area  is 
usually  found  through  that  row  of  rivets  in  the  reinforcing  plate  which 
is  nearest  the  center  of  the  member  (page  208:  2).  Furthermore,  the  mem- 
ber must  extend  beyond  the  pin  far  enough  so  that  the  net  area  of  cross 
section  between  the  pin  and  the  end  of  the  member,  parallel  to  the  axis, 
should  not  be  less  than  the  net  area  of  the  main  member.  In  determin- 
ing the  net  area  at  the  pin,  the  diameter  of  the  hole  is  taken  equal  to  the 
nominal  diameter  of  the  pin,  although  it  is  from  ¥y  to  ¥V"  greater.  Due 
allowance  should  be  made  for  any  reduction  in  area  on  account  of 
flanges  of  channels  or  angles  being  cut  to  clear  eye  bars  or  other 
members. 

2.  The  rivets  in  a  tension  member  should  satisfy  other  requirements 
in  addition  to  those  on  page  285: 1.  When  the  thickness  of  the  reinforcing 
plates  determined  by  the  net  area  exceeds  that  required  for  bearing,  the 
rivets  should  fully  develop  the  strength  of  the  plates  in  tension.  Other- 
wise the  total  number  of  rivets  is  found  as  on  page  285 : 1.  The  rivets  which 
connect  the  reinforcing  plates  to  the  end  of  a  compression  member  are 
naturally  all  placed  on  the  side  of  the  pin  nearer  the  center  of  the  mem- 
ber. This  is  often  necessarily  true  because  the  member  cannot  extend 
beyond  the  pin  without  interfering  with  an  opposing  member.  In  a 
tension  member  the  rivets  must  be  divided.  Enough  rivets  must  be 
placed  in  the  plates  between  the  pin  and  the  center  of  the  member  to 
transmit  the  tensile  stress  in  the  plates  which  is  required  to  develop  the 
necessary  net  section  at  the  pin,  as  explained  in  the  preceding  paragraph. 
But  no  more  rivets  should  be  so  placed  than  can  be  developed  by  the 
actual  tensile  strength  of  the  plates  at  the  pin.  Between  these  minimum 
and  maximum  values  the  number  of  rivets  on  the  side  of  the  pin  toward 
the  center  of  the  member  is  chosen,  and  the  balance  of  the  total  num- 
ber is  placed  between  the  pin  and  the  end  of  the  member.  When  rivets 
are  placed  on  both  sides  of  the  pin  in  a  compression  member  the  distribu- 
tion should  be  determined  in  a  similar  manner. 


CHAPTER   XLII 


REINFORCING  PLATES 


287 


1.  Illustrative  Problem.  —  Tension  Member.  Design  the  reinforcing 
plates  at  the  end  of  a  hanger  composed  of  two  8"  UJ  13J#,  from  which  a 
load  of  110,000#  is  suspended  by  means  of  a  3"  pin,  as  shown  in  Fig.  287. 

Use  a  single  6"  plate  on  each  channel,  f"  rivets,  and  a 

bearing  value  of  20,000#/sq.  in. 


"0  t  K 

""""  "^Iw 

>  € 

CM 

0   O 

) 

< 

O  O 

) 

( 

O   O 

> 

( 

o 

g 

0   0 

1 

0   O 

) 

C  ^ 

55,000# 


0.92' 


110,000  -= 
55,000 


2  =  stress  in  each  web  and  its 
reinforcement 

=  combined  thickness  of  web 


T 


Fig.  287. 


3  x  20,000 

and  plates 

f"  =  0.61"  =0.92-0.31  =  thickness    of    reinforcing 

plate  required  for  bearing 

4.38sq.  in.  =  (4.04  -  2  x  |  X  0.31)1.25  =  net  area  re- 
quired at  pin 

&"  =  0.42"  =  [4.38  -  (4.04  -  3  x  0.31)]  -=-  (6  -  3)  = 

thickness    of    reinforcing 

plate  required  for  tension 

37,500#  =  f  X  3  X  20,000  =  developed      stress      in 


bearing 

21,000#  =  (6  -  3)  x  TV  X  16,000  =  developed  stress  in  tension 
30,000#  =  (6  -  3)  X  f  X  16,000  =  strength  of  plate  in  tension 


9  =  37,500  -=-  4420  =  total  number  of  rivets 
5  =  21,000  -s-  4420  =  minimum  number  of  rivets  above  the  pin 
6+  =  30,000  -^  4420  =  maximum      "        "     "         "       "     " 

The  thickness  required  for  bearing  exceeds  that  required  for  tension  and 
a  6  x  |  plate  is  used.  In  order  to  develop  this  plate  in  bearing  a  total 
of  9  rivets  must  be  used.  In  order  to  develop  the  required  stress  in  ten- 
sion at  least  5  rivets  must  be  placed  above  the  pin  (toward  the  center), 
but  not  more  than  6  can  be  so  placed  without  over  stressing  the  plate  in 
tension.  This  maximum  number  falls  between  6  and  7,  so  the  smaller 
number  is  used.  At  least  5  and  not  over  6  rivets  should  be  placed  above 
the  pin,  the  remainder  being  placed  below.  Since  the  rivets  are  placed 
in  two  rows,  6  are  placed  above  and  4  below,  an  extra  rivet  being  used 
in  order  to  keep  the  member  symmetrical.  The  length  of  the  member 

4  04  —  2  x  ~  X  0  31 
below  the  bottom  of  the  pin  should  be  at  least  3f"  =  - 

0 .  O^  -j-  U .  o  1 

so  that  the  net  area  will  equal  that  of  the  main  member.  If  the  thickness 
of  the  plate  required  for  tension  had  been  greater  than  that  required  for 
bearing,  the  total  number  of  rivets  and  the  maximum  and  minimum 
numbers  above  the  pin  would  be  identical,  and  all  the  rivets  would  be 
placed  above  the  pin.  In  this  case,  a  few  extra  rivets  would  be  used 
below  the  pin  to  hold  the  plate  in  place. 


CHAPTER  XLIII 
BEARING  PLATES  AND   COLUMN  BASES 

SYNOPSIS:  Wherever  structural  steel  is  supported  by  masonry,  some  provision  must 
be  made  to  distribute  the  load  over  the  proper  area  The  design  of  simple  bases  is  dis- 
cussed in  this  chapter. 


1.  Type.  —  Loads  from  steel  beams,  trusses,  or  columns  which  rest 
upon  masonry  must  be  distributed  over  a  sufficient  area  so  that  the  al- 
lowed bearing  value  of  the  masonry  will  not  be  exceeded.     Simple  rec- 
tangular plates  of  steel  or  cast  iron  are  used  under  the  ends  of  beams, 
roof  trusses,  and  some  of  the  lighter  girders.     Cast-iron   pedestals  are 
used  under  the  heavier  girders.     Plate  and  angle  shoes,  with  expansion 
rollers  support  bridge  trusses.     Cast-iron  bases  or  steel  slabs,  in  con- 
junction with  grillage  beams  or  reinforced  concrete  piers,  are  used  under 
office  building  columns,  while  other  columns  are  provided   with  bases 
built  of  plates  and  angles. 

2.  Size  of  Bearing  Plate.  —  Standard  bearing  plates  are  used  at  the 
ends  of  wall-bearing  I-beams  and  channels  under  usual  conditions  for 
the  sake  of  simplicity.     The  sizes  of  these  plates  are  given  in  the  tables 
of  I-beams  and  channels,  pages  298  to  302.     Special  plates  should  be 
designed  for  beams  with. relatively  large  reactions,  for  roof  trusses,  and 
for  light  plate  girders  or  latticed  girders.     The  required  area  of  the  plate 
is  equal  to  the  maximum  reaction  divided  by  the  bearing  value  of  the 
masonry.     The  allowed  pressure  per  square  inch  varies  with  the  differ- 
ent specifications  and  with  the  kinds  of  masonry.     Usual  values  for  con- 
crete are  from  400  to  600  pounds  per  square  inch,  the  latter  value  being 
specified  by  the  American  Railway  Engineering  Association.     For  brick, 
the  values  are  about  one-half  as  large.     The  shape  of  the  plate  which 
will   best    meet   the   requirements   depends   upon   several    factors.     The 
best  distribution  on  the  masonry  is  effected  when  the  two  dimensions  of 


the  plate  are  approximately  equal,  but  this  is  not  always  feasible, 
thickness  of  the  plate  depends  upon  the  distance  the  plate  projects  be- 
yond the  edges  of  the  beam,  and  this  should  be  kept  as  small  as  practical. 
Usually  the  plate  does  not  extend  beyond  the  end  of  the  beam,  and  the 
shorter  dimension  of  the  plate  determines  the  amount  the  beam  pro- 
jects upon  the  supporting  wall.  If  this  is  too  large,  the  length  of  the 
beam  is  unnecessarily  long,  and  if  too  short,  dangerous  cracks  may  develop 
in  the  wall.  The  bearing  plates  of  light  trusses  and  girders  are  usually 
anchored  to  the  masonry,  and  the  plate  must  be  long  enough  to  provide 
the  necessary  edge  distances  beyond  the  bolt  holes  when  the  anchor 
bolts  are  placed  far  enough  from  the  edges  of  the  angles  to  permit  the 
turning  of  the  nuts.  It  may  seem  wise  at  times  to  make  the  area  of  the 
plate  somewhat  greater  than  that  required,  but  the  thickness  may  be 
made  correspondingly  less  because  the  developed  unit  pressure  on  the 
masonry  is  reduced. 

3.  The  thickness  of  a  bearing  plate  should  be  such  that  the  bearing  value 
of  the  masonry  may  be  developed  at  every  point.  The  thickness  is  deter- 
mined by  the  maximum  projection  of  the  plate  beyond  the 
edge  of  the  superimposed  metal.  This  portion  of  the  plate  is 
treated  as  a  cantilever  beam  with  a  uniformly  distributed  pres- 
sure on  the  under  side  equal  to  the  developed  bearing  pressure 
on  the  masonry.  The  maximum  bending  moment  on  this 
portion  of  the  plate  occurs  at  the  edge  of  the  superimposed  metal.  An 
expression  for  the  thickness  may  be  derived,  as  follows  (see  Fig.  288) : 


Fig.  288. 


288 


CHAPTER   XLIII 


BEARING   PLATES  AND   COLUMN   BASES 


289 


Let  b  =  the  developed  unit  stress  in  bearing  on  the  masonry,  i.e.,  the 
total  load  divided  by  the  area  at  the  plate,  in  pounds  per 
square  inch, 
/  =  the  allowed  unit  stress  in  bending  on  the  extreme  fibers  of  the 

plate,  in  pounds  per  square  inch, 
p  =  the  projection  of  the  plate    beyond  the    superimposed  metal, 

in  inches, 

c  =  the  width  of  the  portion  of  the  plate  considered,  in  inches, 
t  =  the  required  thickness  of  the  plate,  in  inches. 

Since  the  pressure  and  the  resisting  moment  are  both  proportional  to  c, 
its  value  does  not  affect  the  result. 

be  =  the  pressure  per  linear  inch,  uniformly  distributed, 

7) 

pbc  X  £  =  the  maximum  bending  moment  in  pound-inches  (page  187: 1), 

f 

\fct~  =  the  resisting  moment  in  pound-inches  (page  199:3). 

By  equating  the  resisting  moment  to  the  bending  moment  and  solving, 
we  have 


36 


nj 


t  = 


The  diagram  on  page  316  gives  values  for  t  to  correspond  to  different 
values   of   p   and    b    when   /  =  16,000#/sq.    in.     For    cast-iron    plates  / 
is  usually  about  3000#/sq.  in.     When  the  load  is  applied 
to  the  plate  by  means  of  angles,  as  in  the  case  of  a  roof 
truss  or  light  girder,  the  combined  thickness  of  the  angle 
and  the  plate  must  be  sufficient  to  prevent  bending  at  the 
-    edge    of   the  vertical   leg   of    the  angle.      This  combined 
Fig.  289  (a).       thickness  t'  may  be  found  from  the  above  formula  by  tak- 
ing p  equal  to  the  distance  from  the  edge  of  the  plate  to 
the  vertical  leg  of  the  angle,  as  shown  by  p',  Fig.  289  (a).     The  fillet  of  the 
angle  is  usually   neglected.     If  the  thickness  of  the  angle  is  fixed,  the 
thickness  of  the  plate  should  be  the  greater  of  two  values,  one  the  thick- 
ness /  required  at  the  edge  of  the  angle,  and  the  other  the   difference 
between  the  combined  thickness  I'  and  the  thickness  of  the  angle. 

] .  Illustrative  Problem.  —  Bearing  Plate.  Design  a  bearing  plate 
for  a  roof  truss  which  rests  upon  a  brick  wall,  as  in  Fig.  114  (d).  The 
bottom  chord  angles  are  5  X  3J  X  f ,  and  they  are  separated  by  a  f " 


heel  plate.  The  maximum  reaction  is  33,000#,  and  the  allowed  unit 
stress  on  the  brick  wall  is  300#/sq.  in.  The  required  area,  110  sq.  in. 
=  33,000  4-  300,  would  be  satisfied  by  a  plate  10"  x  11".-  If  J"  anchor 
bolts  are  used,  the  holes  should  be  punched  about  2"  from  the  edges  of 
the  angles  to  allow  for  turning  the  nuts.  With  an  edge  distance  of  about 
14",  the  length  of  the  plate  must  be  about  1'2£"  =  f  +  2(3£  +  2  +  1J). 
Probably  it  would  be  better  to  increase  the  area  accordingly,  rather 
than  to  reduce  the  10"  bearing  of  the  truss.  The  effect  of  this  in- 
crease would  be  to  reduce  the  developed  bearing  value  6  to  228#/sq.  in. 
=  33,000  -  (10  x  14.5). 
=  4(141  -  I)  -  31,  and 


=  1(14}  -  f)  -  s 


The  projection  beyond  the  angles  is  p  =  3TV 
the    projection    beyond    the    vertical    legs    is 
From    the     diagram,     the     corresponding 
f",  and  the  combined  thickness  of  the 


P'  -  6H 

thickness  of  the  plate  alone  is  t 

plate  and  the  angles  is  I'  =  If".     Since  the  chord  angles  are  only  f "  thick 

the  plate  must  be  at  least  1"  =  If  —  f,  and  since  this  exceeds  the  first 

value  the  size  of  plate  adopted  is  10  x  1  X  1'2%". 

2.  Expansion.  —  At  one  end  of  a  span,  two  plates  may  be  used  in- 
stead of  one  to  allow  free  expansion  or  contraction  under  temperature 
changes.     A  "masonry  plate"  rests  upon  the  masonry,  and  a  "sole  plate" 
is  riveted  to  the  girder  or  truss,  the  surfaces 

of  contact  being  planed.  Slotted  holes  for 
the  anchor  bolts  are  provided  in  the  upper 
plate.  The  combined  thickness  will  be 
somewhat  greater  than  the  thickness  of  a 
single  plate,  because  each  plate  is  designed 
to  resist  its  proportion  of  the  total  bending 
moment.  Thus  if  the  two  plates  are  of 
equal  thickness,  each  would  be  about  0.7 
=  V$  of  the  thickness  required  for  a  single 
plate. 

3.  Pedestals  and  Shoes.  —  Bridge  girders 
are    commonly   supported   by   cast-iron   or 
cast -steel  pedestals,  as  shown  in  Fig.  289  (b). 

These  pedestals  are  fastened  to  the  masonry  by  anchor  bolts,  and  the 
girders  are  bolted  to  them.  Slotted  holes  are  provided  in  one  end  of 
girders  up  to  about  60  feet  in  length  to  allow  for  expansion,  the  top  of 
the  pedestals  and  the  bottoms  of  the  bearing  plates  on  the  girders  being 


\ 

ZDC\ 

Fig.  289  (6).  'Cast  Pedestal  for 
Bridge  Girder. 


290 


PART   III  — THE   DESIGN   OF  DETAILS 


planed.  Segmental  rollers  are  placed  under  the  pedestal  at  one  end  of 
girders  over  60  feet  long.  Special  hinged  shoes  or  rockers  are  used  at  the 

ends  of  some  of  the 
longer  girders  to  pre- 
vent unequal  distribu- 
tion of  the  load  upon 
the  masonry  as  the 
girders  deflect.  Similar 
hinged  shoes  are  used 
at  the  ends  of  bridge 
trusses,  and  roller  nests 
are  placed  under  the 
shoes  at  one  end,  as 
shown  in  Fig.  290.  For 
the  design  of  shoes  and 
rollers  consult  books  on 
Bridge  Designing,  par- 
ticularly those  listed 
below.* 

1.   Column  bases  are 
Fig.  290.    Typical  Bridge-truss  Shoe  with  Rollers.          of  two  main  types  which 

for  convenience  will  be 

designated  according  to  the  principal  structures  in  which  they  are  used, 
viz.:  mill  buildings  and  office  buildings.  In  the  former  the  loads  are 
transmitted  largely  by  rivets,  while  in  the  latter  by  direct  bearing.  In 
mill  buildings  the  column  loads  are  comparatively  light,  and  the  bases 
must  be  anchored  to  the  masonry  piers  to  prevent  lateral  displacement 
by  accident,  and  to  resist  the  overturning  effect  of  the  wind.  Cross 
bracing  can  be  used  only  at  the  ends  of  a  mill  building,  and  the  wind 
pressure  on  the  sides  must  be  resisted  largely  by  the  columns  acting  as 
beams  fixed  at  the  lower  ends.  The  effect  of  this,  combined  with  the 
effect  of  eccentric  loading  on  the  column,  is  to  cause  unequal  distribution 
of  the  load  on  the  masonry,  and  the  area  of  the  base  must  be  so  propor- 
tioned that  at  no  point  will  the  allowed  bearing  pressure  be  exceeded. 

*  Waddell's  "Bridge  Designing,"  Vols.  I  and  II,  John  Wiley  and  Sons,  Inc.,  New 
York,  and  Skinner's  "Details  of  Bridge  Construction,"  Vol.  Ill,  McGraw-Hill  Book 
Co.,  Inc.,  New  York. 


The  pressure  near  one  edge  of  the  base  may  be  very  small,  in  fact  the 
upward  forces  due  to  wind  may  exceed  the  downward  forces  due  to  the 
direct  load  so  that  it  is  necessary  to  anchor  the  base  to  the  masonry.  In 
order  to  make  the  anchor  bolts  effective,  the  base  must  be  securely  riveted 
to  the  column,  and  for  this  reason  it  is  usually  built  of  plates  and  angles. 
For  light  columns,  such  as  shown  in  Fig.  137,  these  rivets  are  designed 
to  transmit  the  whole  column  loads.  Columns  which  support  crane  run- 
ways or  other  moving  loads,  and  columns  in  which  the  load  exceeds  40,^09 
pounds  are  milled  so  that  a  portion  of  the  loads  are  transmitted  by  direct 
bearing.  A  typical  crane-girder  column  base  is  shown  in  Fig.  135.  In 
office  buildings  there  are  intermediate  columns  which  are  rigidly  con- 
nected at  each  floor,  and  the  principal  wind  stresses  which  reach  the 
basement  columns  are  vertical.  The  uplift  on  the  windward  columns 
is  usually  less  than  the  vertical  dead  loads  so  that  anchors  are  not  re- 
quired except  in  tall  narrow  buildings  or  towers.  From  the  nature  of 
the  building  there  is  slight  chance  of  displacement  of  the  column  bases 
by  accident.  The  bending  stresses  are  small  compared  to  the  total  loads, 
and  the  pressure  on  the  bases  is  distributed  more  uniformly  than  in  mill 
buildings.  Cast-iron  or  cast-steel  bases,*  such  as  shown  in  Fig.  175  («), 
are  commonly  used  in  office-building  construction.  The  bottoms  of  the 
columns  and  the  tops  of  the  cast  bases  are  both  planed  so  that  practically 
the  entire  column  loads  are  transmitted  by  direct  bearing  without  rivets. 
Light  angles  are  usually  riveted  to  the  end  of  the  column,  as  in  ABl, 
Fig.  133,  and  these  angles  are  bolted  to  the  cast  bases  to  prevent  displace- 
ment during  erection.  The  cast  bases  are  grouted  on  top  of  reinforced 
concrete  piers  or  grillage  beams,  as  explained  in  the  next  chapter  (see 
Fig.  291),  and  then  they  are  imbedded  in  concrete.  Column  bases  are 
usually  standardized  by  structural  companies  so  that  it  is  unnecessary 
to  design  each  base.  Furthermore,  the  design  depends  so  much  upon 
the  wind  stresses,  that  it  seems  unwise  to  attempt  further  explanation 
here.f 

*  For  dimensions  of  American  Bridge  Company's  standard  cast  bases  see  Ketchum's 
"Structural  Engineers'  Handbook,"  McGraw-Hill  Book  Company,  Inc.,  New  York. 

f  For  the  design  of  mill-building  column  bases,  see  Kirkham's  "Structural  Engineer- 
ing," McGraw-Hill  Book  Co.,  Inc.,  New  York;  for  the  comparison  of  different  methods  ol 
designing  anchor  bolts,  see  articles  by  R.  Fleming  and  E.  Godfrey  in  the  Engineering 
News,  April  30,  1914,  and  May  7, 1914;  for  the  design  of  cast  bases  for  office  buildings 
see  Burt's  "Steel  Construction,"  American  Technical  Society,  Chicago. 


CHAPTER  XLIV 
GRILLAGE  BEAMS 

SYNOPSIS:  When  it  is  impractical  to  extend  foundations  for  heavily  loaded  columns 
to  bed  rock,  the  footings  may  be  spread  over  the  proper  area  of  soil  within  a  compara- 
tively small  depth  by  means  of  grillage  beams  imbedded  in  concrete. 


1.  When  Used.  —  In  providing  suitable  foundations  for  office  build- 
ings it  is  often  impractical,  if  not  impossible,  to  extend  the  footings  to 
bed  rock.     When  the  footing  of  an  average  office-building  column  bears 
directly  on  the  soil  a  large  bearing  area  is  required  because  of  the  com- 
paratively small  pressure  allowed  on  the  soil.     If  an  ordinary  masonry 
pier  were  designed  to  satisfactorily  distribute  the  load  from  the  small 
area  at  the  column  base  to  the  large  area  required  on  the  soil,  the  pier 
would  be  so  deep  that  the  cost  of  the  excavation  and  of  the  masonry 
would  be  prohibitive.     The  same  results  may  be  obtained  in  much  less 
depth  by  the  use  of  either  steel  grillage  beams  or  reinforced  concrete  slabs. 
The  design  of  reinforced  concrete  footings  would  be  out  of  place  in  this 
book.     Grillage  beams  are  still  in  common  use  since  reinforced  concrete 
footings  have  not  yet  met  with  universal  favor  for  various  reasons,  among 
them  being  the  uncertain  effects  of  electrolysis  and  corrosion  upon  the 
comparatively  small  steel  areas  in  the  reinforcing  rods. 

2.  Arrangement.  —  Grillage  beams  are  arranged  in  tiers,  as  shown  in 
Fig.  291,  the  beams  in  one  tier  being  placed  at  right  angles  to  those  in 
the  next  tier.     The  bottom  tier  rests  upon  a  concrete  mat  about  12  inches 
thick.     Concrete  is  placed  between  the  beams  of  each  tier,  and  ultimately 
the  whole  footing,  including  the  cast-iron  base,  is  imbedded  in  concrete 
at  least  4  inches  thick  to  hold  the  parts  in  position  and  to  protect  the  steel 
against  fire   and  corrosion.     The   concrete   between  the  beams  acts  as 
inverted  arches  to  complete  the  bearing  area  of  the  tier.     The  maximum 
distance  in  the  clear  between  the  beams  should  be  such  that  the  full  pres- 
sure on  the  concrete  is  transmitted  to  the  beams.     Unless  this  clear  dis- 


tance between  the  edges  of  the  flanges  exceeds  about  one  and  one-half 
times  the  width  of  each  flange  it  is  unnecessary  to  investigate  the  strength 


Fig.  291.     Grillage  Footing  (Concrete  Filling  Not  Shown). 

of  the  arch.*    The  spacing  of  the  beams  is  usually  determined  by  the 

number  to  be  placed  within  a  given   distance.     The  distance   between 

*  For  the  method  of  investigation,  see  page  201:3. 


291 


292 


PART   III  — THE   DESIGN   OF  DETAILS 


flanges  should  be  at  least  1\  or  3  inches  to  permit  the  placing  and  the 
tamping  of  the  concrete.  Since  it  is  difficult  to  insure  uniform  bearing 
between  the  beams  of  successive  tiers  when  they  are  placed  in  contact,  a 
space  of  about  f  inch  is  usually  left  for  grouting.  Similarly,  if  the  unit 
load  is  not  too  great,  grout  is  used  between  the  upper  beams  and  the 
cast  base.  This  facilitates  placing  the  base  truly  horizontal  and  at  the 
proper  elevation.  The  allowed  pressure  on  the  grout  is  about  35  tons 
per  square  foot,  or  500  pounds  per  square  inch.  If  the  column  load 
divided  by  the  area  at  the  bottom  of  the  cast  base  exceeds  this  amount, 
the  base  must  be  placed  in  direct  contact  with  the  beams,  the  bottom  of 
the  base  being  planed.  This  requires  extreme  accuracy  in  setting  the 
beams  to  furnish  uniform  bearing  for  the  base  at  the  proper  elevation. 

1.  Tie  Rods.  —  Grillage  beams  are  held  at  uniform  distances  apart  by 
means  of  rods  and  separators.     When  it  is  not  feasible  to  use  beams 
with  webs  thick  enough  to  withstand  the  tendency  to  buckle,  cast-iron 
separators  or  stiffening  angles  may  be  used  to  stiffen  the  webs.     Usually, 
however,  pieces  of  gas  pipe  are  placed  between  the  webs.     Three-fourths 
inch  rods  extend  through  all  the  beams  of  each  tier,  passing  through  the 
separators  (Fig.  291).     Enough  rods  should  be  used  to  resist  the  thrust 
of  the  concrete  arches  between  the  beams  (preceding  paragraph).     It  is 
seldom  necessary  to  calculate  this  thrust.     Usually  rods  are  placed  about 
6  inches  from  the  ends  of  the  beams,  and  the  remaining  spaces  are  sub- 
divided so  that  the  rods  are  not  more  than  5  or  6  feet  apart.     In  the 
smaller  beams  the  rods  are  placed  centrally  in  the  webs;    in  beams  12 
inches  or  more  in  depth  the  rods  are  used  in  pairs,  the  vertical  spacing 
being  the  same  as  for  cast-iron  separators  (page  316). 

2.  The  loads  for  which  grillage  beams  are  designed  are  determined  by 
one  of  several  methods.*    A  grillage  foundation  will  settle  as  the  loads 
are  applied;  this  cannot  be  prevented.     It  is  important  that  the  settle- 
ment be  uniform  throughout  the  structure  to  prevent  cracks  in  the  walls 
and  floors.     Under  like  soil  conditions  this  means  that  the  unit  pressure 
must  be  the  same  for  all  footings.     Some  engineers  design  each  footing 
for  the  total  dead  and  live  load,  while  others  design  the  footing  for  the 
critical  column  and  proportion  the  others  from  this  one  according  to  the 

*  For  comparison,  see  Jacoby  and  Davis'  "Foundations  of  Bridges  and  Buildings," 
McGraw-Hill  Book  Co.,  Inc.,  New  York. 


ratios  that  the  dead  loads  bear  to  the  dead  load  of  the  critical  column, 
maintaining  that  the  settlement  will  be  proportional  to  the  dead  loads 
because  they  act  at  a  maximum  constantly.  The  critical  column  is  the 
one  which  has  the  largest  ratio  of  dead  load  to  live  load.  Other  engi- 
neers consider  one-half  (or  other  fraction)  of  the  live  load  in  conjunction 
with  the  dead  load  in  determining  the  ratios.  The  live  load  on  the  base- 
ment column  is  not  the  sum  of  the  maximum  live  loads  from  each  floor, 
but  a  certain  percentage  of  this  sum  depending  upon  the  height  of  the 
building.f 

3.  The  allowed  bearing  pressure  should  be  determined  by  tests  made 
upon  the  actual  material  at  the  site.     Records  of  tests  made  for  nearby 
buildings  are  sometimes  available.     Average  values  for  different  charac- 
ters of  soil  as  specified  in  different  building  codes  are  tabulated  in  both 
of  the  books  just  referred  to.     These  values  are  usually  expressed  in 
tons  per  square  foot.     They  may  be  converted  into  pounds  per  square 
inch  by  multiplying   by  13.89  =  2000  +  144,  or   approxi mutely  by  mul- 
tiplying by  14. 

4.  The  extreme  dimensions  of  the  concrete  mat  are  determined  by  the 
area  found  by  dividing  the  total  load  by  the  allowed  pressure  on  the 
soil.     The  most  desirable  shape  of  mat  is  a  square,  but  it  is  not  always 
possible  to  use  a  square  of  sufficient  proportions  without  extending  beyond 
the  building  lines  or  interfering  with  other  foundations  or  pits.     Usually 
a  rectangular  mat  will  prove  satisfactory.     In  case  it  is  impracticable  to 
center  the  grillage  under  the  column,  the  eccentricity  may  be  overcome 
by  means  of  a  cantilever  girder  {  which  extends  under  an  adjacent  column. 
The  extreme  dimensions  of  the  bottom  tier  of  beams  may  be  made  less 
than  the   corresponding  dimensions  of  the   concrete  mat,   because  the 
mat  itself  may  be  considered  to  partially  distribute  the  load.     The  re- 
sisting moment  of  the  concrete  depends  upon  the  tensile  strength  in  the 
extreme  fiber;   this  is  variable  and  very  small.     A  projection  of  6  inches 
on  each  side  of  a  mat  12  inches  thick  is  considered  safe,  but  an  increase 
in  this  amount  would  be  inadvisable.     It  may  be  found  that  when  a 

t  See  copies  of  the  building  laws  of  different  cities,  or  Ketchum's  "Structural  En- 
gineers' Handbook,"  McGraw-Hill  Book  Co.,  Inc.,  New  York. 

I  See  Kidder's  "Architects'  and  Builders'  Pocket  Book,"  John  Wiley  and  Sons,  Inc., 
New  York. 


CHAPTER   XLIV 


GRILLAGE   BEAMS 


293 


projection  of  one-half  the  depth  of  the  mat  is  used,  the  tensile  stress  in 
the  extreme  fiber  is  three-fourths  of  the  bearing  power  of  the  soil.* 

1.  Method  of  Design.  —  Grillage  beams  must  be  designed  to  resist 
bending,  buckling,  and  shearing.     The  depth  of  a  beam  is  usually  deter- 
mined by  bending,  and  the  web  thickness  either  by  bending  or  buckling. 
The  upper  beams  are  first  designed  for  bending  and  then  their  strength  is 
investigated  regarding  buckling  and  shear.     It  may  not  be  necessary  to 
consider  either  buckling  or  shear  in  the  design  of  the  lower  tiers.     Many 
different  arrangements  of  grillage  beams  may  be  designed  to  satisfy  given 
conditions,  because  the  beams  of  the  different  tiers  are  interdependent. 
The  best  arrangement  may  be  selected  from  the  results  of  several  differ- 
ent designs,  with  due  consideration  of  the  comparative  costs.     Usually 
two  or  three  tiers  will  suffice.     The  extreme  width  of  the  top  tier  of  beams 
is  equal  to  the  corresponding  dimension  of  the  column  base.     The  length 
of  the  beams  in  one  tier  is  equal  to  the  extreme  width  of  the  next  tier  be- 
low.    If  only  two  tiers  are  used,  the  length  of  the  top  beams  is  equal  to 
the  extreme  width  of  the  bottom  tier.     If  it  is  impractical  to  make  the 
top  beams  so  long,  an  intermediate  tier  is  used,  the  length  of  which  is 
equal  to  the  width  of  the  bottom  tier.     The  width  of  this  intermediate 
tier,  equal  to  the  length  of  the  top  tier,  is  made  such  that  the  top  beams 
have  equal  strength  in  resisting  bending  and  buckling. 

2.  Design  for  Bending.  —  The  number  of  beams  to  be  used  in  any 
tier  is  unknown.     For  this  reason  it  is  convenient  to  compute  the  total 
bending  moment  on  all  the  beams  in  the  tier,  and  from  this  bending  mo- 
ment find  the  combined  section  modulus.     The  proper  numbers  of  beams 
of  different  sizes  may  then  be  found  which  will  furnish  the  required  sec- 
tion modulus,  and   the   best  combination  may  be  selected.      The  total 
downward  load  on  each  tier  of  beams  is  equal  to  the  column  load  W. 
It  is  uniformly  distributed  throughout  the  central  portion  of  all  the  beams 
for  a  distance  L'  equal  to  the  extreme  width  of  the  superimposed  tier  of 
beams,  if  any,  or  to  the  width  of  the  column  base.     The  beams  are  sup- 
ported by  upward  forces  of  the  same  total  magnitude  (W)  but  these  forces 
are  uniformly  distributed  throughout  the  entire  length  of  the  beams  L. 
The  weight  of  the  beams  may  be  neglected.     The  maximum  bending 


/3h 
As  in  the  design  of  bearing  plates  (page 288: 3)  t  =  p  I/  — ,  whence  /  =  |6  if  t  =  2p. 


moment  will  occur  at  the  center.  An  expression  for  the  maximum  bend- 
ing moment  for  all  the  beams  in  the  tier  may  be  found  by  the  method  of 
page  187 : 1 .  The  downward  forces  at  the  left  of  the  center  may  be  replaced 

W  L' 

by  a  single  resultant  force  of  -=-  acting  at  a  distance  of  -r-  from  the  center. 

^  4 

W 

Similarly,  the  resultant  of  the  upward  forces  is  -=-  but  it  acts  at  a  distance 

,  L  ,  W      L      W      L' 

of  j-  from  the  center.     The  bending  moment  is  -^-  X  -. 5-  X  -r,  or 

4  A        4         « 

W  W 

j  (L  -  L')  =  Afat,  or  j  (Z  -  I')  =  ma 

The  combined  section  modulus  of  all  the  beams  in  the  tier  may  be  found 
by  dividing  this  bending  moment  by  the  allowed  unit  stress  in  bending. 
The  section  modulus  should  be  equaled  or  exceeded  by  the  product  of  the 
number  of  beams  and  the  section  modulus  of  a  single  beam. 

3.  Investigation  for  Buckling.  —  The  portions  of  the  beam  webs  di- 
rectly below  the  superimposed  load  act  as  columns  and  they  should  be 
of  sufficient  thickness  to  prevent  buckling.  The  usual  column  formulas 
(page  211:2)  in  terms  of  I  and  r  are  inconvenient,  but  they  may  be  con- 
verted into  equivalent  formulas  in  terms  of  d  and  t,  where  d  is  the  depth 
of  the  beam  and  t  the  web  thickness.  The  effective  length  I  may  be 
safely  taken  as  0 . 825d  which  is  slightly  greater  than  the  average  tangent 
distance  between  the  curved  fillets  connecting  the  flanges  to  the  web. 
The  formula  for  unit  stress  is  independent  of  the  area  of  cross  section  of  the 
column  so  we  may  assume  a  portion  of  beam  x  inches  in  length.  The  area 
of  cross  section  of  the  column  is  then  te  and  the  least  moment  of  inertia 

xf 
is  T-^,  whence  the  least  radius  of  gyration  r 

Substituting  these  values  for  I  and  r  in  the  column  formula  16,000  —  70  - 


/~T          /  xt?          ' 
=  i/  —  =  \/  ^^  =  -^=- 


we  have  16,000  - 


70  x  0.825d 
t 


or 


t  Note  that  the  bending  moment  is  a  function  of  the  projection  of  the  beam  beyond 
the  superimposed  load.  The  bending  moment  is  equivalent  to  the  bending  moment 
at  the  center  of  a  simple  beam  under  the  same  total  load,  uniformly  distributed,  for  a 
span  equal  to  this  projection  (L-L1), 


294 


PART   III  — THE   DESIGN   OF   DETAILS 


16,000  -  200  -  =  the  allowed  unit  stress 

I 

per  square  inch  of  web  section  under  direct  load.  Compare  page  201 : 2. 
This  web  section  is  the  product  of  the  number  of  beams  in  a  tier  by  the 
thickness  of  the  web  and  by  the  distance  (in  inches)  over  which  the  super- 
imposed load  is  distributed.  By  some  companies  this  distance  is  in- 
creased by  one-quarter  or  one-half  the  depth  of  the  beam,  part  of  the 
web  beyond  the  load  being  considered  effective. 

1.  Investigation  for  Shear.  —  The  maximum  shear  on  a  grillage  beam 
will  occur  at  the  outer  edge  of  the  superimposed  load.     Its  magnitude 
may  be  found  by  multiplying  the  distance  (in  inches)  which  the  beam 
projects  at  each  end  beyond  the  superimposed  load  by  the  upward  force 
per  linear  inch  of  beam.     This  upward  force  is  found  by  dividing  the 
total  column  load  by  the  number  of  beams  in  the  tier  and  by  the  length 
of  each  beam.     The  maximum  intensity  of  shear  per  square  inch  is  found 
by  dividing  the  above  magnitude  by  the  area  of  cross  section  of  the 
portion  of  the  web  between  the  flanges  (page  202: 1).     This  intensity  of 
shear  should  not  exceed  the  unit  stress  in  shear  allowed  by  the  specifica- 
tions, as  for  example  10,000#/sq.  in. 

2.  Illustrative  Problem.  —  Design  a  grillage  footing  for  a  column  load 
of  400,000#,  using  the  following  unit  stresses 

3T/sq.  ft.  =  42#/sq.  in.  =  allowed  bearing  value  on  soil 

500#/sq.  in.  =  "       "  grout 

16,000#/sq.  in.  =  unit  stress  in  bending 
10,000#/sq.  in.  =     "         "      "  shear 

16,000  -  200  pf /sq.  in.  =  "      "  buckling. 

Assuming  that  a  square  footing  can  be  used,  each  side  of  the  12"  con- 
„          /400,000 
'V  ~ 


crete  mat  should  be  98' 


-,  and  allowing  a  6"  projection  be- 


yond the  beams,  the  length  of  the  bottom  beams  is  86"  =  98  -  2  x  6. 


Each  side  of  a  square  cast-iron  base  should  be  28.3"  =/ 


/400,000  . 


500 


if  grout 


is  to  be  used.     Many  companies  make  their  bases  in  multiples  of  3"  to 
minimize  the  number  of  different  patterns.     We  will  use  a  30"  square  base. 


First  Arrangement  —  Two  Tiers 

If  two  tiers  of  beams  are  used  as  in  Fig.  291,  the  length  of  each  is  86". 
The  load  on  the  upper  tier  will  be  distributed  over  30",  the  width  of  the 


column   base.     The   total    section  modulus   is    175  = 


400,000 


(86  -  30) 


-f-  16,000.  We  can  use  either  4  -  15"  Is  42#(s  =  236)  or  4  -  12"  Is 
40#(s  =  179).  The  clear  distances  between  flanges  are  2.7"  =  (30  -  4 
X  5|)  +  3,  and  3.0"  =  (30  -  4  x  5|)  H-  3,  respectively.  Smaller  beams 
need  not  be  tried  because  more  than  four  would  be  required  and  the 
space  between  flanges  would  be  too  small.  The  12"  Is  40#  are  chosen 
because  they  are  lighter,  and  the  webs  are  less  liable  to  buckle.  The  direct 

stress  which  -tends  to  buckle  the  webs  is  7200#/sq.   in.  =        4PP'°C 

which  is  safely  under  the  allowed  unit  stress  of  10,800#/sq.  in.  =  16,000 

200  x  12 

intensity      is      7700#/sq.   in. 


0.46 
400,000  x  *  (86  -  30) 


The     maximum     shear 


which   is  less  than  the   10,000   allowed.     The 


4x86(12-2xlf)0.46 
beams  selected  are  therefore  satisfactory.  The  total  section  modulus 
for  the  beams  in  the  lower  tier  is  the  same  as  for  those  in  the  upper  tier, 
since  both  /  and  I'  are  the  same.  The  conditions  are  fulfilled  by  any 
one  of  the  following  combinations: 


Number  of 
Beams 

Size 

Section 
Modulus 

Total  \Veight 
per  foot 

Clear  Distance 
between  Flanges 

5 

12'    I  31J# 

180 

158 

15.3'    =  (86  -  5  x  5.0)  *  4 

7 

10'   I  30# 

188 

210 

8.7'    =  (86  -7  x4.8)  ^6 

8 

10'   I25# 

195 

200 

6.9'    =  (86  -8  x4.7)  -*•  7 

10 

9'  I  21# 

189 

210 

4.7'    =  (86  -  10  x4.4)  +9 

13 

8'   I  18# 

185 

234 

2.8'    =  (86  -13  X4.0)  -5-12 

The  5-12"  Is  3l%"  are  the  lightest  and  they  involve  the  smallest  number 
of  pieces  to  be  handled,  but  they  are  too  far  apart.  The  7-10"  Is  30#  are 
also  too  far  apart,  and  they  weigh  more  than  the  8-10"  Is  25#.  The 
latter  best  meet  the  requirements  and  they  are  strong  enough  to  resist 

400,000  200  x  10 


both  buckling  and  shear  because 


8  X  30  x  0.31 


<  16,000  - 


0.31 


and 


CHAPTER   XLIV 


GRILLAGE  BEAMS 


295 


400,000  X  \  (86-30) 


8  X  86  x  10  X  0.31 

arrangement  is  2580  =  (4  x  40  +  200)86 


<  10,000.     The  total  weight  of  the  beams  for  this 
12. 


Second  Arrangement  —  Three  Tiers 

It  is  obvious  that  the  upper-tier  beams  will  be  smaller  than  those  in 
the  first  arrangement  because  they  are  shorter.  In  order  to  make  the 
beams  of  equal  strength  in  resisting  bending  and  buckling,  let  us  first 
design  them  to  resist  buckling  and  then  determine  their  proper  length. 
The  safe  loads  of  different  sizes  of  beams  are  as  follows: 


Number  of 
Beanu 

Size 

Safe 

Load  Determined  by  Resistance 
to  Buckling 

4 
4 
4 

10"  I  25# 

9"  I  25# 
8"  I  20J# 

355,000#  = 
570,000#  = 

(  16  000     200xl°") 

4  x  30  x  0.31 
4  x  30x0.41 
4  x  30  x  0.36 

k     '               0.31     ) 
"lOOOO      200x9N| 

<'™           0.41    J 

'  Hi  000      20°  x  8^ 

L1<yW          0.36   J 

The  safe  load  of  the  10"  Is  25#-is  less  than  400,000#  so  they  cannot  be 
used.  4-10"  Is  30#  would  be  sufficient  but  these  would  weigh  more 
than  the  4-9"  Is  25#  so  they  need  not  be  investigated.  5-8"  Is  18#  would 
be  sufficient  but  they  would  weigh  more  than  4-8"  Is  203#.  The  latter 
are  the  lightest  beams  which  will  satisfy  the  conditions.  The  distance 
between  flanges  is  4.5"  -  (30  -  4  X  4.1)  +  3.  The  safe  length  of  these 
beams  in  bending  may  be  found  by  equating  an  expression  for  ms  to  w/e 
400  000 


thus: 
49". 


O 


(I  -  30)  =  4  x  15.2  x  16,000,    whence   I  =  49.5"  or   say 


These  beams  are  also  strong  enough  to  resist  the  shear,  because 


10'°00' 


selected'     The 


total  section  modulus  for  the  middle  tier  is  the  same  as  in  the  bottom  tier 
of  the  first  arrangement,  because  the  /  and  the  V  are  the  same.  The 
beams  may  be  selected  from  those  shown  under  the  first  arrangement, 
but  the  same  ones  cannot  be  used  because  they  would  be  too  close  together. 
Either  5-12"  Is  3l£#  or  7-10"  Is  30#  could  be  used,  the  former  being 
lighter.  The  distance  between  flanges  is  6"  =  (49  -  5  x  5.0)  H-  4.  These 
12"  beams  are  strong  enough  to  resist  both  buckling  and  sheai  because 

400.000        ,  m  QQO      200  x  12  400,000  x  j(86  -  30) 

5x30x0.3,^  16>(X1  0.35  '    5x86  (12-2  xl|)0.35<   10'00°- 

The    total    section    modulus    for    the    beams    in    the    bottom    tier    is 


116 


400,000 


(86  -  49)  +  16,000.     The    following    beams    give    the   re- 


quired section  modulus: 


Xumber  of 

Section 

Total  Weight 

Clear  Distance 

Beams 

Modulus 

per  foot 

between  Flanges 

7 

9"  I  21# 

132 

147 

9.3"  =  (86  -7  x4.4)  +6 

9 

8"  I  18# 

128 

162 

6.2"  =  (86  -9  x4.0)  *8 

11 

7"  I  15# 

114 

165 

3.9"  -  (86  -  11  x  3.7)  *  10 

Either  the  8"  or  the  7"  beams  are  satisfactory,  but  the  9"  beams  would 
be  too  far  apart.  The  9-8"  Is  18#  are  chosen  because  they  are  lighter. 
It  is  usually  unnecessary  to  investigate  the  strength  of  the  bottom  beams 
for  buckling  or  for  shear,  because  of  the  relatively  large  number.  The 
total  weight  of  the  beams  for  this  arrangement  is  2630#  =  (4  x  20j 
X  49  +  5  x  3H  X  86  +  9  X  18  X  86)  +  12.  This  is  only  slightly  more 
than  the  weight  of  the  beams  for  the  first  arrangement  but  there  are  four 
more  beams  to  handle,  and  the  depth  of  the  excavation  and  the  amount 
of  concrete  is  more.  This  can  be  shown  roughly  by  comparing  the  ex- 
treme depth  of  steel  allowing  1"  between  tiers  for  grouting,  thus: 
23"  =12  +  1  +  10  for  the  first  arrangement  and  30"  =  8  +  1+12  +  1+8 
for  the  second.  In  general  two  tiers  are  preferred  to  one,  and  the  first 
arrangement  would  be  used,  as  shown  in  Fig.  291. 


TABLES  AND   DIAGRAMS 

For  Description,  see  pages  334-338. 


297 


298 


WEIGHTS  AND  DIMENSIONS  OF  CARNEGIE  I-BEAMS  AND  AMERICAN  BRIDGE  COMPANY  CONNECTION  ANGLES. 


V  

iM 

1 

IF  THICKNESS  OF  WEB  OR  WIDTH  OF  FLANGE  IS  MORE  THAN  £  ABOVE  AN  EVEN 
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USE  i  "RIVETS  IN  THE  CONNECTION  ANGLES 

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:ROSS  SECTION  BY  THE  AREA  OF  AN  ADDITIONAL  RIVET  HOLE 
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MINIMUM    PITCHES   FOR    FLANGE    RIVETS 


UNIT  STRESSES 
POUNDS   PER  SQUARE  INCH 

RIVETS  IN   A  SINGLE   LINE 

RIVETS  STAGGERED   IN   TWO   LINES 

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U 

H 

H 

21 
21 

21 
21 

2ft 

2ft 
2i 

IK 

2! 

** 

U 

2 

H 

21 

11 
li 

11 

H 

U 
li 

H 
li 

IH 

2T 

ii 

2j 

21 

21 

li 

81 

2 

BEARING  IN  WEB                                         b  =22,000 

i 

2H 

2H 

2H 

2ft 

2ft 

2ft 

2ft 

2 

2H 

2H 

2H 

2H 

2H 

i 

21 

81 

21 

2 

U 

U 

H 

M 

21 

2i 

n 

2S 

156 

3ft 

3ft 

3ft 

3ft 

2j 

21 

2ft 

21 

3ft 

3ft 

3ft 

3ft 

3ft 

156 

2H 

2H 

2H 

2ft 

2} 

21 

IH 

2H 

2H 

2H 

2H 

2« 

at 

3H 

:<!! 

3H 

3! 

3! 

3ft 

3 

25 

3H 

3H 

3!!, 

3H 

3H 

1(4 

3 

3 

3 

2H 

2H 

21 

2ft 

3 

3 

1 

3 

3 

% 

i  A 

1ft 

1ft 

1ft 

1ft 

1ft 

1ft 

1ft 

11 

IH 

1ft 

li 

1A 

% 

ift 

1ft 

1ft 

1ft 

1ft 

1ft 

1  ,'„ 

li 

1ft 

1ft 

H 

1ft 

SHEAR  ON  WEB    (NET  SECTION)           s   =  12,000 
SHEAR  ON   RIVETS                                       s'  =  10,000 

ft 

2ft 

2ft 

li 

2i 

li 

2ft 

It 

2 

li 
U 

U 

iH 

!'« 

li 

21 
2ft 

21 

2ft 

2ft 
2ft 

IH 

2ft 

15 
SI 

"ft 

H 

1ft 

21 

1ft 

2H 

H 

H 

H 
H 

H 
H 

H 
H 

IH 

IH 

li 

H 

1ft 

21 

IH 

IH 

1.H 

IH 

IH 

BEARING   IN  WEB                                         b  =  20,000 

i 

2H 

2H 

21 

2ft 

2ft 

2ft 

2ft 

2 

2H 

2H 

2H 

2H 

2H 

l 

2} 

21 

2ft 

H 

H 

it 

H 

21 

21 

2} 

2} 

81 

156 

31 

31 

31 

2H 

2{ 

2ft 

2ft 

2f 

31 

31 

31 

31 

31 

at 

21 

21 

21 

2ft 

21 

iH 

MS 

2} 

21 

si 

2! 

21 

154 

3ft   3ft 

3ft 

3ft 

3ft 

3 

25 

2} 

3ft 

3ft 

3ft 

3ft 

3ft 

154 

2i 

21 

2| 

2} 

21 

2ft 

2i 

3| 

2i 

2i 

2! 

NO    VALUE    GIVEN    IS    LESS    THAN    THE    MINIMUM    SPACING    FOR    MACHINE    DRIVEN    RIVETS,    EQUAL    TO    THE    DIAMETER    OF    THE    RIVET    HEAD    PLUS    i". 
VALUES    ABOVE    THE    SHORT    FINE    LINES    ARE    LESS    THAN    THE    MINIMUM    STAGGER    FOUND    FROM    THE    DIAGRAM    ON    THE    PRECEDING    PAGE    FQR    GAGE   0  =  2}".! 
FOR    THE    MINIMUM    STAGGER    FOR    OTHER    GAGES,    SEE    DIAGRAM. 

MULTIPLICATION  TABLE  FOR   RIVET  SPACING 


307 


SPACES 

PITCH    OF    RIVETS    IN    INCHES 

|  SPACES 

4 

4 

H 

H 

»l 

U 

4 

2 

4 

»i 

4 

*i 

4 

4 

4 

3 

si 

4 

4 

31 

4 

4 

41 

4 

«f 

1 

«i 

4 

•I 

6 

1 

21 

2} 

21 

3 

3! 

3} 

31 

4 

4} 

4} 

41 

5 

5} 

5} 

51 

6 

6} 

6} 

6! 

7 

7} 

8 

8} 

9 

9} 

10 

10} 

11 

11} 

1-0 

i 

3 

31 

31 

4} 

4} 

4! 

5i 

5! 

6 

H 

6} 

7J 

7} 

7! 

8} 

81 

9 

9} 

9} 

10! 

10} 

Hi 

1-0 

1-0} 

1-1} 

1-2} 

1-3 

1-3} 

1-4} 

1-5} 

1-6 

3 

4 

4} 

5 

5} 

6 

6} 

7 

7} 

8 

8} 

9 

9} 

10 

10} 

11 

11} 

1-0 

1-0} 

1-1 

1-1} 

1-2 

1-3 

1-4 

1-5 

1-6 

1-7 

1-8 

1-9 

1-10 

1-11 

2-0 

4 

5 

H 

6t 

« 

7} 

81 

K 

91 

10 

10! 

11} 

Hi 

1-0} 

i-U 

1-1} 

1-2! 

1-3 

1-3! 

1-4} 

1-4! 

1-5} 

1-6} 

1-8 

1-9} 

1-10} 

i-lli 

2-1 

2-2} 

2-3} 

2-*l 

2-« 

6 

6 

61 

7} 

81 

9 

91 

10} 

1H 

1-0 

i-oi 

1-1} 

1-2} 

1-3 

1-3} 

1-4} 

1-51 

1-6 

1-6! 

1-7} 

1-8} 

1-9 

1-10} 

2-0 

2-1} 

2-3 

2-4} 

2-6 

2-7} 

2-9 

2-10} 

3-0 

6 

7 

H 

81 

91 

10} 

HI 

1-0} 

1-1} 

1-2 

1-2! 

1-3} 

l-«l 

1-5} 

1-6! 

1-71 

1-8} 

1-9 

l-9i 

1-10} 

i-iii 

2-0} 

2-2} 

2-4 

2-5} 

2-7} 

2-9} 

2-11 

3-01 

3-2} 

3-4} 

3-6 

7 

8 

9 

10 

11 

1-0 

1-1 

1-2 

1-3 

1-4 

1-5 

1-6 

1-7 

1-8 

1-9 

1-10 

1-11 

2-0 

2-1 

2-2 

2-3 

2-4 

2-6 

2-8 

2-10 

3-0 

3-2 

3-4 

3-6 

3-8 

3-10 

4-0 

8 

9 

10i 

lit 

i-oi 

1-1} 

1-2| 

1-3J 

1-H 

1-6 

1-71 

1-8} 

1-91 

1-10} 

1-111 

2-0} 

2-H 

2-3 

2-4} 

2-5} 

2-6} 

2-7} 

2-9} 

3-0 

3-2} 

3-4} 

3-6} 

3-9 

3-11} 

4-1} 

4-3} 

4-6 

9 

10 

Hi 

1-OJ 

I-U 

1-3 

1-41 

1-5} 

1-6} 

1-8 

1-9} 

1-10} 

1-1  U 

2-1 

2-2} 

2-31 

2-4} 

2-6 

2-7} 

2-8} 

2-9} 

2-11 

3-1} 

3-4 

3-6} 

3-9 

3-11} 

4-2 

4-4} 

4-7 

4-9} 

5-0 

10 

11 

1-Oi 

1-11 

1-31 

1-4} 

1-5} 

1-71 

l-8i 

1-10 

1-111 

2-0} 

2-2! 

2-3} 

2-4! 

2-6} 

2-7} 

2-9 

2-10! 

2-1  H 

3-H 

3-2} 

3-5} 

3-8 

3-10} 

4-1} 

4-4} 

4-7 

4-9} 

5-0} 

5-3} 

5-6 

11 

12 

i-U 

1-3 

UJ 

1-6 

1-7} 

1-9 

1-10} 

2-0 

2-1} 

2-3 

2-4} 

2-6 

2-7} 

2-9 

2-10} 

3-0 

3-1} 

3-3 

3-4} 

3-6 

3-9 

4-0 

4-3 

4-6 

4-9 

5-0 

5-3 

5-6 

5-9 

6-0 

12 

13 

1-2J 

1-*} 

1-5! 

1-7} 

1-9} 

1-10J 

2-0} 

2-2 

2-3J 

2-5} 

2-6J 

2-8} 

2-10i 

2-11} 

3-1! 

3-3 

3-4| 

3-6} 

3-71 

3-»} 

4-0} 

4-4 

4-7} 

4-10} 

5-1} 

5-5 

5-8} 

5-11} 

6-2} 

6-6 

13 

14 

1-3} 

1-5} 

1-71 

1-9 

1-101 

2-0} 

2-2J 

2-4 

2-5! 

2-7} 

2-91 

2-11 

3-0} 

3-2} 

3-4} 

3-6 

3-7} 

3-9} 

3-11} 

4-1 

4-4} 

4-8 

4-11} 

5-3 

5-6} 

5-10 

6-1} 

6-5 

6-8} 

7-0 

14 

15 

1-4! 

1-61 

1-8| 

1-10} 

2-01 

2-2} 

2-41 

2-6 

2-7} 

2-9} 

2-11J 

3-1} 

3-3| 

3-5} 

3-7! 

3-9 

3-10J 

4-0} 

4-21 

4-4} 

4-8} 

5-0 

5-3} 

5-7} 

5-11} 

6-3 

6-6} 

6-10} 

7-2} 

7-6 

15 

16 

1-6 

1-8 

1-10 

2-0 

2-2 

2-4 

2-6 

2-8 

2-10 

3-0 

3-2 

3-4 

3-6 

3-8 

3-10 

4-0 

4-2 

4-4 

4-6 

4-8 

5-0 

5-4 

5-8 

6-0 

6-4 

6-8 

7-0 

7-4 

7-8 

8-0 

16 

17 

1-7} 

1-9} 

1-111 

2-1} 

2-3f 

2-5} 

2-7J 

2-10 

3-0} 

3-2} 

3-4} 

3-6} 

3-8| 

3-10} 

4-0} 

4-3 

4-5} 

4-7} 

4-9! 

4-11} 

5-3} 

5-8 

8-0} 

6-J} 

6-8} 

7-1 

7-5} 

7-9} 

8-1} 

8-6 

17 

18 

l-8i 

1-10} 

2-OJ 

2-3 

2-51 

2-7} 

2-9| 

3-0 

3-2} 

3-4} 

3-6! 

3-9 

3-11} 

4-1} 

4-3} 

4-6 

4-8} 

4-10} 

5-0} 

5-3 

5-7} 

6-0 

6-4} 

6-9 

7-1} 

7-6 

7-10} 

8-3 

8-7} 

9-0 

18 

19 

1-9| 

1-111 

2-2} 

2-4} 

2-6! 

2-9} 

2-11! 

3-2 

3-4! 

3-6} 

3-9} 

3-11} 

4-U 

4-4} 

4-6J 

4-9 

4-11} 

s-U 

5-4} 

5-6} 

5-11} 

6-4 

6-8} 

7-1} 

7-6} 

7-11 

8-3} 

8-8} 

9-1} 

9-6 

19 

20 

1-10} 

2-1 

2-3} 

2-6 

2-8} 

2-11 

3-1} 

3-1 

3-6} 

3-9 

3-11} 

4-2 

4-4» 

4-7 

4-9} 

5-0 

5-2} 

5-5 

5-7} 

5-10 

6-3 

6-8 

7-1 

7-6 

7-11 

8-4 

8-9 

9-2 

9-7 

10-0 

20 

21 

l-ll! 

2-2} 

2-11 

2-7} 

2-101 

3-01 

3-3| 

3-6 

3-8| 

3-11} 

4-U 

4-4} 

4-7} 

4-9} 

5-0} 

5-3 

5-5! 

5-8} 

5-10J 

6-1} 

6-6} 

7-0 

7-5} 

7-10} 

8-3} 

8-9 

9-2} 

9-7} 

10-0} 

10-6 

21 

22 

2-OJ 

2-3} 

2-61 

2-9 

2-111 

3-2} 

3-5} 

3-8 

3-10} 

4-1} 

4-1} 

4-7 

4-9} 

5-0} 

5-3} 

5-6 

5-8} 

5-11} 

6-2} 

6-5 

6-10} 

7-4 

7-9} 

8-3 

8-8} 

9-2 

9-7} 

10-1 

10-6} 

11-0 

22 

23 

2-U 

2-4} 

2-7J 

2-10} 

3-1J 

3-4} 

3-7} 

3-10 

4-OJ 

4-3} 

4-6! 

4-9J 

5-0} 

5-3} 

5-6} 

5-9 

5-11! 

6-2} 

6-5} 

6-8} 

7-2} 

7-8 

8-1} 

8-7} 

9-1} 

9-7 

10-0} 

10-6} 

11-0} 

11-6 

23 

24 

2-3 

2-6 

2-9 

3-0 

3-3 

3-6 

3-9 

4-0 

4-3 

4-6 

4-9 

5-0 

5-3 

5-6 

5-9 

6-0 

6-3 

6-6 

6-9 

7-0 

7-6 

8-0 

8-6 

9-0 

9-6 

10-0 

10-6 

11-0 

11-6 

12-0 

24 

25 

2-U 

2-71 

2-10| 

3-1} 

3-4| 

3-7} 

3-10! 

4-2 

4-5} 

4-81 

4-11} 

5-2} 

5-5! 

5-8} 

5-11! 

6-3 

6-6} 

6-9} 

7-0} 

7-3} 

7-9} 

8-4 

8-10} 

9-4} 

9-10} 

10-5 

10-111 

11-5} 

11-11} 

12-6 

26 

26 

2-5J 

2-8} 

2-111 

3-3 

3-6J 

3-9} 

4-0} 

4-4 

4-7} 

4-10} 

5-1} 

5-5 

5-8} 

5-11} 

6-2} 

6-6 

6-9} 

7-OJ 

7-3} 

7-7 

8-1} 

8-8 

Ml 

9-9 

10-3} 

10-10 

11-4} 

11-11 

12-5} 

13-0 

26 

27 

2-6| 

2-91 

3-H 

3-4} 

3-7J 

3-11} 

4-2! 

4-6 

4-9! 

5-0} 

6-41 

5-7} 

5-10J 

6-2} 

6-5! 

6-9 

7-0} 

7-3} 

7-7} 

7-10} 

8-5} 

9-0 

9-6} 

10-1} 

10-8} 

11-3 

11-9} 

12-4} 

12-11} 

13-6 

27 

28 

2-7} 

2-11 

3-2} 

3-6 

3-9} 

4-1 

4-1} 

4-8 

4-11} 

5-3 

5-6} 

5-10 

6-1} 

6-5 

6-8} 

7-0 

7-3} 

7-7 

7-10} 

8-2 

8-9 

9-4 

9-11 

10-6 

11-1 

11-8 

12-3 

12-10 

13-6 

14-0 

28 

29 

2-8| 

3-0} 

3-3J 

3-7} 

3-11} 

4-21 

4-6! 

4-10 

5-H 

5-5} 

5-8! 

6-0} 

6-4} 

6-7} 

6-lli 

7-3 

7-6! 

7-lOj 

8-U 

8-5} 

9-0} 

9-8 

10-3} 

10-10} 

11-5} 

12-1 

12-8} 

13-3} 

13-10} 

14-6 

29 

30 

2-9  1 

3-1J 

3-5} 

3-9 

4-01 

4-4} 

4-8} 

5-0 

5-31 

5-7} 

5-11} 

6-3 

6-«} 

6-10} 

7-2} 

7-« 

7-9} 

8-1} 

8-5} 

8-9 

9-4} 

10-0 

10-7} 

11-3 

11-10} 

12-6 

13-1} 

13-9 

14-4} 

15-0 

30 

4 

li 

4 

4 

If 

U 

4 

2 

4 

4 

4 

4 

4 

*i 

4 

3 

4 

4 

4 

4 

3! 

4 

4 

4 

4 

5 

•{ 

»* 

4 

6 

308 


•  I"  RIVET  VALUES 


SHEARING   AND   BEARING   VALUES   FOR   |"   RIVETS   IN  THOUSANDS  OF   POUNDS 

BEARING    VALUES    TO    THE    LEFT    OF    THE    DOTTED    LINES    ARE    LESS    THAN    THE    SINGLE    SHEAR    VALUES                                            8       RIVETS 
BEARING  VALUES  IN  PLATES  THICKER  THAN  THOSE  GIVEN  ARE  GREATER  THAN  THE  DOUBLE  SHEAR  VALUES 

SHOP    RIVETS 

FIELD    RIVETS 

BOLTS 

NO. 
OF 
RIVS 

SHEAR    AT 
12000  LBS./SQ.  IN 

BEARING  IN  PLATE  AT  24000  LBS./SQ.  IN. 

NO. 
OF 
RIVS 

SHEAR    AT 
10000  LBS./SQ.  IN 

BEARING  IN  PLATE  AT  20000  LBS./SQ.  IN. 

NO. 
OF 
RIVS 

SHEAR    AT 
9000  LBS./SQ.  IN 

BEARING  IN  PLATE  AT  18000  LBS./SQ.  IN. 

SINGLE 

DOUBLE 

A        i 

A 

3 
8 

A 

SINGLE 

DOUBLE 

A        i 

A 

i 

A 

SINGLE 

DOUBLE 

i 

A 

1 

A 

1 

2 
3 

4 
S 

6 
7 
8 
9 
10 

3.7 
7.4 
11.0 
14.7 
18.4 

22.1 
25.8 
29.5 
33.1 
36.8 

7.4 
14.7 
22.1 
29.5 
36.8 

44.2 
51.5 
58.9 
66.3 
73.6 

2.8           3.8 
5.6           7.5 
8.4         11.3 
11.3         15.0 
14.1         18.8 

16.9         22.5 
19.7         26.3 
22.5         30.0 
25.3         33.8 
28.1         37.5 

4.7- 
9.4 
14.1 
18.8 
23.4 

28.1 
32.8 
37.5 
42.2 
46.9 

5.6 
11.3 
16.9 
22.5 
28.1 

33.8 
39.4 
45.0 

50.6 
56.3 

6.6 
13.1 
19.7 
26.2 
32.8 

39.4 
45.9 
52.5 
59.1 
65.6 

1 

2 
3 

4 
5 

6 
7 
8 
9 
10 

3.1 
6.1 
9.2 
12.3 
15.3 

18.4 
21.5 
24.5 
27.6 
30.7 

6.1 
12.3 
18.4 
24.5 
30.7 

36.8 
43.0 
49.1 
55.2 
61.4 

2.3           3.1 
4.7            6.3 
7.0            9.4 
9.4          12.5 
11.7          15.6 

14.1          18.8 
16.4         21.9 
18.8         25.0 
21'.1          28.1 
23.4         31.3 

3.9 

7.8 
11.7 
15.6 
19.5 

23.4 
27.3 
31.3 
35.2 
39.1 

4.7 
0.4 
14.1 

18.8 
23.4 

28.1 
32.8 
37.5 
42.2 
46.9 

5.5 
13.9 
16.4 
21.9 
27.3 

32.8 
38.3 
43.8 
49.2 

54.7 

1 

2 
3 

4 
6 

6 
7 
8 
9 
10 

2.8 
5.5 
8.3 
11.0 
13.8 

16.6 
19.3 
22  1 
24.8 
27.6 

5.5 
11.0 
16.6 
22  1 
27.6 

33.1 
38.7 
44.2 
49.7 
55.2 

2.1            2.8 
4.2           5.6 
6.3           8.4 
8.4          11.2 
10.6          14.1 

12.7         16.9 
14.8         19.7 
16.0         22.5 
19.0         25.3 
21.1         28.1 

3.5 
7.0 
10.5 
14  1 
17.6 

21.1 
24.6 
28.  1 
31.6 
35.2 

4.2 
8.4 
12.7 
16.9 
21.1 

25.3 
29.5 
33.8 
38.0 
42.2 

4.9 
9.8 
14.8 
19.7 
24.6 

29.5 
34.5 
39.4 
44.3 

49.2 

SHOP    RIVETS 

FIELD    RIVETS 

BOLTS 

NO. 
OF 
RIVS. 

SHEAR    AT 
11000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  22000  LBS./SQ.  IN. 

NO. 
OF 
RIVS. 

SHEAR  AT 
9000  LBS./SQ.  IN. 

BEARING  IN  PLATEAT18000  LBS./SQ.  IN. 

NO. 
OF 

RIVS. 

SHEAR    AT 
8000  LBS./SQ.  IN 

BEARING  IN  PLATEAT16000  LBS./SQ.  IN 

SINGLE 

DOUBLE 

A              i 

A 

1 

A 

SINGLE 

DOUBLE 

A        i 

A 

3 

S 

A 

SINGLE 

DOUBLE 

A              1 

A 

I 

A 

1 
2 
3 
4 
5 

6 
7 
8 
9 
10 

3.4 
6.8 
10.1 
13.5 
16.9 

20.3 
23  6 
27.0 
30.4 
33.8 

6.8 
13.5 
20.3 
27.0 
33.8 

40.5 
47.3 
54.0 
60  8 
67.5 

2.6           3.4 
5.2           6.9 
7.7          10.3 
10.3         13.7 
12.9         17.2 

155         20.6 
18.0         24.1 
20.6         27.5 
23.2         30.9 
25.8  .       34.4 

4.3 

8.6 
12.9 
17.2 
21.5 

25.8 
30.1 
34.4 
38.7 
43.0 

5.2 
10.3 
15.5 
20.6 
25.8 

30.9 
36.1 
41.2 
46.4 
51  6 

6.0 
12.0 
18.0 
24. 
30. 

36. 
42. 
48. 
54. 
60.2 

1 
2 
3 

4 
5 

6 
7 
8 
9 
10 

2.8 
5.5 
8.3 
11.0 
13.8 

16.6 
19.3 
22.1 
24.8 
27.6 

5.5 
11.0 
16.6 
22.1 
27.6 

33.1 

38.7 
44.2 
49.7 
55.2 

2.1           2.8 
4.2           5.6 
6.3           8.4 
8.4          11.2 
10.6         14.1 

12.7          16.9 
14.8         19.7 
16.9         22.5 
19.0        x25.3 
21.1          28.1 

3.5 
7.0 
10.5 
14.1 

17.6 

21.1 
24.6 
28.1  . 
31.6 
35.2 

4.2 
8.4 
12.7 
16.9 
21.1 

23.3 
29.5 
33.8 
38.0 
42.2 

4.9 
9.8 
14.8 
19.7 
24.6 

29.5 
34.5 
39.4 
44.3 

49.2 

1 
2 
3 

4 
5 

6 
7 
8 
9 
10 

2.5 
4.9 
7.4 
9.8 
12.3 

14.7 
17.2 
19.6 
22.1 
H.I 

4.9 

9.8 
14.7 
19.6 
24.5 

29.5 
34.4 
39.3 
44.2 

49.1 

1.9           2.5 
3.8           5.0 
5.6          7.5 
7.5         10.0 
9.4         12.5 

11.3          15.0 
13  1          17.5 
15.0         20.0 
16.9         22.5 
18.8         25.0 

3.1 

63 
9.4 
12.5 
15.6 

18.8 
21.9 
25.0 
28.1 
31.3 

3.8 
7.5 
11  3 
15.0 
18.8 

22.5 
26.3 
30.0 
33.8 
37.5 

4.4 
8.8 
13.1 
17.5 
21.9 

26.3 
30.6 
35.0 
39.4 
43.8 

SHOP    RIVETS 

FIELD    RIVETS 

BOLTS 

NO. 
OF 
RIVS. 

SHEAR   AT 
10000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  20000  LBS./SQ.  IN. 

NO. 
OF 
RIVS. 

SHEAR    AT 
8000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT16000  LBS./SQ.  IN. 

NO. 
OF 
RIVS. 

SHEAR   AT 
7000  LBS./SQ.  IN. 

BEARING  IN  PLATEAT14000  LBS./SQ.  IN. 

SINGLE 

DOUBLE 

A        i 

A 

i 

A 

SINGLE 

DOUBLE 

A        i 

A 

1 

A 

SINGLE 

DOUBLE 

A              i 

A 

I 

A 

1 
2 
3 
4 
6 

6 
7 
8 
9 
10 

3.1 
61 

9.2 
12.3 
15  3 

18.4 
21.5 
24.5 
27.6 
30.7 

6.1 
12.3 

18.4 
24.5 
30.7 

36.8 
43.0 
49.1 
55.2 
61.4 

2.3           3.1 
4.7           6.3 
7.0           9.4 
9.4          12.5 
11.7          15.6 

14.1          18.8 
16.4         21.9 
18.8         25.0 
21.1         28.1 
23.4         31.3 

3.9 
7.8 
11.7 
15.6 

19.5 

23.4 
27.3 
31.3 
35.2 
39.1 

4.7 
9.4 
14.1 
18.8 
23.4 

28  1 
32.8 
37.5 
42.2 
46.9 

5.5 
10.9 

16.4 
21.9 
27.3 

32.8 
38.3 
43.8 
49.2 
54.7 

1 
2 
3 
4 
5 

6 
7 
8 
9 
10 

2.5 
4.9 
7.4 
9.8 
12.3 

14.7 
17.2 
19.6 
22.1 
24.5 

4.9 
9.8 
14.7 
19.6 
24.5 

29.5 
34.4 
39.3 
44.2 
49.1 

1.9           2.5 
3.8           5.0 
5.6           7.5 
7.5         10.0 
9.4         12.5 

11.3         150 
13.1         17.5 
15.0         20.0 
16.9         22.5 
18.8         25.0 

3.1 

6.3 
9.4 
12.5 
15.6 

18.8 
21.9 
25.0 
28.1 
31.3 

3.8 
7.5 
11.3 
15.0 
18.8 

22.5 
26.3 
30.0 
33.8 
37.5 

4.4 

8.8 
13  1 
17.5 
21.9 

26.3 

30.6 
35  0 
39.4 
43.8 

1 

2 
3 
4 
5 

6 

7 
8 
9 
10 

2.2 
4.3 
6.4 
8.6 
10.7 

12.9 
15.0 

17.2 
19.3 
21.5 

43 
8.6 
12.9 
17.2 
21.5 

25.8 
30.1 
34.4 

38.7 
43.0 

1.8           2.2 
3.3           4.4 
4.9           6.6 
6.6           8.8 
8.2          10.9 

9.8         13.1 
11.5          153 
13.1          175 
14.8         19.7 
16.4         21.9 

2.7 

5.5 
8.2 
10.9 
13.7 

16.4 
19.1 
21.9 
24.6 
27.3 

3.3 

6.6 
9.8 
13.1 
16.4 

19.7 
23.0 
26  3 
29.5 
32.8 

3.8 

7.7 
11.5 
15.3 
19.1 

23.0 
26.8 
30.6 
34  5 
38.3 

O  .  t> 


I"   RIVET   VALUES 


309 


SHEARING  AND   BEARING   VALUES   FOR  f"   RIVETS   IN   THOUSANDS   OF   POUNDS 
«      RIVETS                                         BEARING    VALUES    TO    THE    LEFT    OF    THE    DOTTED    LINES    ARE    LESS    THAN    THE    SINGLE    SHEAR    VALUES                                         I      RIVETS 
BEARING  VALUES  IN  PLATES  THICKER  THAN  THOSE  GIVEN  ARE  GREATER  THAN  THE  DOUBLE  SHEAR  VALUES 

SHOP   RIVETS 

FIELD   RIVETS 

BOLTS 

NO. 
OF 
RIVS 

SHEAR    AT 
12000  LBS./SQ.  IN 

BEARING  IN  PLATE  AT  24000  LBS./SQ.  IN. 

NO. 
OF 
RIVS 

SHEAR  AT 
10000  LBS./SQ.  IN 

BEARING  IN  PLATE  AT  20000  LBS./SQ.  IN. 

NO. 
OF 

RIVS. 

SHEAR  AT 
9000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  18000  LBS./SQ.  IN. 

SINGLE 

DOUBLE 

A 

i     A 

1 

A 

} 

A 

SINGLE 

DOUBLE 

A 

i     A 

1 

A 

! 

A 

SINGLE 

DOUBLE 

ft 

*      A 

1 

A 

i 

A 

10 

53 
10  6 
15  .9 
21.2 
26  5 

31  8 
37  1 
42  4 

47.7 
53  0 

10  6 
21.2 
31.8 
42  4 
53.0 

63  6 

74.2 
84  .8 

<i:>  4 
106  n 

3.4 
6.8 
10.1 
13  5 

16.9 

20  3 
23.6 
27.0 
30  4 

3.1  S 

45       5.6 
90      11.3 

135     169 
18.0     22.5 
22.5     28  1 

27.0     33.8 
31.5     39.4 
360     45.0 
405     50.6 
450     56.3 

6.8 
13.5 
20.3 
27.0 
33  8 

40.5 
47.3 

54  II 
60.8 
67  5 

7.9 
15.8 
23  6 
31.5 
39.4 

47  3 
55.1 
63.0 
70.9 
78.8 

9.0 
18.0 
27.0 
36  0 
45.0 

54.0 
63.0 
72.0 
81.0 

!>(!  0 

10.1 
20.3 
30.4 
40.5 
50.6 

60.8 
70.9 
81.0 
91.1 

Illl   :; 

6 
7 
8 
9 
10 

4.4 
8.8 
13.3 

17.7 
22.1 

26.5 
30.9 
35.3 
39.8 
44.2 

8.8 
17.7 
26.5 
35.3 

44.2 

53.0 
61.9 

70.7 
79.5 

xs  4 

2.8 
5.6 
8.4 
11.3 
14.1 

16.9 
19.7 
22.5 
25.3 
28.1 

US       4.7 
7.5      9.4 
11  3     14.1 
15.0     18.8 
18.8     23.4 

22.5     28.1 
26.3     32.8 
30.0     37.5 
33.8     42.2 
37.5     469 

5.6 
11.3 
16.9 
22.5 
28.1 

33.8 
39.4 
45.0 
50.6 
56  3 

66 
13.1 
19.7 
26.3 
32.8 

39.4 
45  9 
52.5 
59.1 
65.6 

7.5 
15  0 
22.5 
30.0 
37.5 

45.0 
52.5 
60.0 

67.5 

75  () 

8.4 
16  9 
25.3 
33.8 
42.2 

50.6 
59.1 
67.5 
75.9 

S4  4 

10 

4.0 
8.0 
11.9 
15.9 
19.9 

23  9 
27.8 
31.8 
35.8 
39  8 

8.0 
15.9 
23.9 
31.8 
39.8 

47.7 
55.7 
63  6 
71.6 

79.5 

2.5 
5.1 
7.6 
10.1 
12.7 

15.2 
17.7 
20.2 
22.8 
25.3 

34       4.2 
68      84 
10.1     12.7 
135     16.9 
169     21.1 

20.3     25.3 
23.6     29.5 
270     338 
304     38.0 
33  8     42.2 

"     J 

w.i 

15  2 
20  3 

25.3 

30.4 
35  4 

40  5 
45.6 

5(1  ti 

5.9 
11.8 
17.7 
23.6 
29.5 

35.4 
41  3 

47.2 
53.2 

.V      1 

6.8 
13.5 
20.3 
27.0 
33.8 

40.5 
47.3 

54  0 
60.8 
67.5 

7  ti 
15.2 
22.8 
30  4 
38.0 

45,6 
53.2 
60.8 
68.3 
75.9 

SHOP    RIVETS 

FIELD   RIVETS 

BOLTS 

NO. 
OF 
RIVS 

SHEAR  AT 
11000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  22000  LBS./SQ.  IN. 

NO. 

OF 
RIVS. 

SHEAR  AT 
9000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  18000  LBS./SQ.  IN. 

NO. 
OF 

RIVS. 

SHEAR  AT 
8000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  16000  LBS./SQ.  IN. 

SINGLE 

DOUBLE 

:i 
To 

i     A 

I 

A 

i 

A 

SINGLE 

DOUBLE 

A 

i  |  A 

t 

A 

i 

A 

SINGLE 

DOUBLE 

A 

i     A 

i 

A 

i 

A 

1 
2 
3 
4 
6 

6 
7 
8 
9 
10 

4  ft 
9  7 
14  6 
19.4 

24.3 

29.2 
34  0 
38  9 
43  7 

48  6 

9.7 
19.4 
29.2 
38.9 
48.6 

58  3 
68.0 
77.8 
87.5 
97.2 

3.1 
6.2 
9.3 
12.4 
15.5 

18.6 

21.7 
24.8 
27.8 

30  11 

4.1       5.2 

8.3     10.3 
12.4     15.5 
16.5     20.6 
20.6     25.8 

24.8     30.9 
28.9     36.1 
33.0     41.2 
37.1     46.4 
41  3     51.6 

6.2 

12.4 
18.6 
24.8 
30.9 

37.1 
43  3 
49.5 
55.7 
61.9 

7.2 
14.4 
21.7 
28.  9 
30.1 

43.3 
50.5 
57.8 
65.0 
72.2 

8.3 

10.5 
24.8 
33.0 
41.3 

49.5 
57.8 
66.0 
74.3 

SL'   :> 

9.3 
18.6 
27.8 
37.1 
46.4 

55.7 
65.0 
74.2 
83.5 
92.8 

8 
9 
10 

4.0 
8.0 
11.9 
15.9 
19.9 

23.9 
27.8 
31.8 
35.8 
39.8 

80 
15.9 
23  9 
31  8 

39.8 

47.7 
55.7 
63  6 
71.6 
79.5 

2.5 
51 
7.6 
10  1 
12.7 

f5.2 

17.7 
29.2 
22.8 
25.3 

34!    42 
6.8  I    8.4 
10  1  !  12  7 
13.5  !  16.9 
16.9  !  21  1 

20.3  I  25.3 
23.6  •  29.5 
27.0  ;  33.8 
30.4  i  38.0 
33  8  J42.2 

5.1 
10.1 
15.2 
20.3 
25  3 

30  4 
35.4 
40.5 
45  6 
50  6 

5.9 
11.8 
17.7 
23.6 
29  5 

35.4 
41  3 

47.2 
53.2 
59.1 

6.8 
13  5 
20.3 
27.0 
33.8 

40.5 
47.3 
54.0 
60.8 
67.5 

7.6 
15.2 
22.8 
30.4 
38.0 

45.6 
53.2 

(10  S 
(IS  3 
75.9 

6 
7 
8 
9 
10 

3.5 
71 
10.6 
14  1 
17.7 

21.2 
24.7 
28.3 
31  8 
35.3 

7.1 
14.1  ' 
21.2 
28  3 
35.3 

42.4 
49.5 
56  6 
63.6 
70.7 

2.3 
4.5 
6.8 
9.0 
11.3 

13.5 
15.8 
18.0 
20.3 
22.5 

3.0      3.8 
8.0      7.5 
90     113 
12.0     15.0 
15.0     188 

180     22.5 
21.0     263 
24.0     300 
27.0     33.8 
30.0     37.5 

45 
9.0 
13  5 
18.0 
22.5 

27.0 
31  5 
36  0 
40.5 
45.0 

53 
10.5 
15.8 
21  0 
26.3 

31.5 
36  8 
42  0 
47.3 

f>2  5 

6.0 
12.0 
18.0 
24.0 
30.0 

36.0 
42  0 
48  0 
54.0 
60.0 

6.8 
13.5 
20.3 
27.0 
33.8 

40.5 
47.3 
54  0 

60  .8 

117  5 

SHOP    RIVETS 

FIELD   RIVETS 

BOLTS 

NO. 
OF 

RIVS 

SHEAR  AT 
10000  LBS     CQ.  IN. 

BEARING  IN  PLATE  AT  20000  LBS./SQ.  IN. 

NO. 
OF 
RIVS. 

SHEAR  AT 
8000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  16000  LBS./SQ.  IN. 

NO. 
OF 

RIVS. 

SHEAR  AT 
7000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  14000  LBS./SQ.  IN. 

SINGLE 

DOUBLE 

A 

\             '?,; 

f 

A 

i 

A 

SINGLE    DOUBLE 

A 

i     ft 

I 

A 

i 

2 

A 

SINGLE 

DOUBLE 

A 

i        A 

1 

A 

i 

A 

1 
2 
3 

4 
5 

6 

7 
8 
9 
10 

4.4 

8.8 
13  3 

17.7 
22.1 

26  5 
30.9 
35.3 
39.8 
44  2 

8.8 
17.7 
26.5 
35  3 
44  2 

53  0 
61.9 
70.7 
79.5 
88.4 

2.8 
5.0 
84 
11  3 
14  1 

16.9 
19.7 
22.5 
25  3 
28.1 

3.8      4.7 
7.5       9.4 
11.3     14.1 
15.0     18.8 
18.8     23.4 

22.5     28.1 
26.3     32.8 
300     375 
33.8     42.2 
37.5     46.9 

5.6 
11.3 
16.9 

22.5 
28.1 

33  8 
39.4 
45.0 
50  6 
56.3 

6.6 
13.1 
19.7 
26.3 
32.1 

39.4 
45.9 
52.5 
69.  1 

65.6 

7.5 
15.0 

22.5 
30.0 
37.5 

45.0 
52.5 
60.0 
67.5 
75.0 

8.4 
16.9 
25.3 
33.8 
42.2 

50.6 
59.1 
67.5 
75.9 
84.4 

6 
7 
8 
9 
10 

3.5 

7.1 
10.6 

14.1 
17.7 

21.2 
24.7 
28.3 
31.8 
35.3 

7.1 
14.1 
21.2 
28.3 
35.3 

42.4 
49.5 
56.6 
63  6 

70.7 

2.3 

4.5 
6.8 
9.0 
11.3 

13.5 

15.8 
18.0 
20.3 
22  5 

3.0      3.8 
6.0       7.5 
9.0      11.3 
12.0     150 
15.0      18.8 

180     225 
21.0     26.3 
24.0     300 
27.0     33.8 
300     375 

4.5 
9.0 
13.5 
18.0 
22.5 

27.0 
31.5 
36  0 
40.5 
45  0 

5.3 

10.5 
15.8 
21  0 
26.3 

31  5 
36.8 
42.0 
47.3 
52.5 

6.0 
12.0 
18.0 
24.0 
30.0 

36.0 
42.0 
48.0 
54  0 
60.0 

6.8 
13.5 
20.3 
27.0 
33.8 

40.5 
47.3 
54.0 
60  8 
67.5 

10 

3.1 

62 
93 
12.4 
15.5 

18.6 
21.7 
24.7 
27.8 
30.9 

6.2 
12  4 
18.6 
24.7 
30.9 

37  1 
43.3 
49  5 
56  7 
61.9 

2.0 
3.9 
5.9 
7.9 

9.8 

11.8 
13  8 
15.8 
17.7 
19.7 

2.6      3.3 
5.3       6.6 
7.9      9.8 
105     13.1 
13  1     16.4 

15.8     19.7 
18.4     23.0 
21.0     26.3 
23.6     29.5 
263     32.8 

3.9 
7.9 
11.8 
15.8 
19.7 

23  6 
27.6 
31  5 
35.4 
39.4 

4.6 
9.2 
13.8 
18  4 
23.0 

27.6 
32.2 
36  8 
41  3 
45.9 

5.3 
10  5 
15  8 
;21  0 
26.3 

31.5 

»i  s 
42  0 
47.3 
52.5 

5.9 
11.8 
17  7 
23.6 
29.5 

35.4 
41.3 
47.2 
53.2 
59.1 

310 


I"   RIVET  VALUES 


SHEARING  AND   BEARING   VALUES   FOR  g"   RIVETS   IN  THOUSANDS   OF   POUNDS 

g       RIVETS                                               BEARING    VALUES    TO    THE    LEFT    OF    THE    DOTTED    LINES    AFIE    LESS    THAN    THE    SINGLE    SHEAR    VALUES                                            §       RIVETS 

BEARING  VALUES  IN   PLATES  THICKER  THAN  THOSE  GIVEN  ARE  GREATER  THAN  THE  DOUBLE  SHEAR  VALUES 

SHOP    RIVETS 

FIELD.  RIVETS 

BOLTS 

NO. 
OF 

SHEAR   AT 
12000  LBS.,  SO..  IN. 

BEARING  IN  PLATE  AT  24000  LBS./SQ   IN. 

NO. 

OF 

SHEAR  AT 
10000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  20000  LBS./SQ.  IN. 

NO. 
Or" 

SHEAR  AT 
9000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  18000  LBS./SQ.  IN. 

RIVS. 

SINGLE 

DOUBLE 

1 

4 

A         I 

A 

i 

A 

! 

RIVS. 

SINGLE 

DOUBLE 

1 

4 

A      I 

A 

i 

A 

5 

RIVS. 

SINGLE 

DOUBLE 

t 

ft     i 

A 

i 

A 

1 

1 

7.2 

14  4 

53 

6.6       7.9 

9.2 

10.5 

11.8 

13.1 

6.0 

12.0 

4.4 

5.5       6.6 

7.7 

s.s 

9.8 

10.9 

1 

5.4 

10.8 

39 

49       5.9 

6.9 

7.9 

8.9 

9.8 

2 

14.4 

28.9 

10.5 

13  1     158 

18.4 

21.0 

23.6 

26.3 

12.0 

24.1 

8.8 

10.9     13.1 

15.3 

17.5 

19.7 

21.9 

2 

10.8 

21  6 

7.9 

9.8     118 

13.8 

15  8 

17.7 

19.7 

3 

21.6 

43.3 

15.8 

10.7     23.6 

27.6 

31.5 

35.4 

39.4 

18.0 

36.1 

13.1 

164     19.7 

23.0 

26.3 

29.5 

32.8 

3 

16.2 

32.5 

11  .8 

14.8     17.7 

20.7 

23.6 

26.6 

29.5 

4 

28.9 

57.7 

21.0 

263     31.5 

36  8 

42.0 

47.2 

52.5 

24. 

48.1 

17.5 

21.9     26.3 

30.6 

35.0 

39.4 

43.8 

4 

21.6 

43.3 

15.8 

19.7     236 

27.6 

31.5 

35.4 

39.4 

5 

36  1 

72.2 

26  3 

32.8     39.4 

45.9 

52.5 

59.1 

65.6 

30. 

60.1 

21.9 

27.3     32.8 

38.3 

43.8 

49.2 

54.7 

1 

27.1 

54.1 

19.7 

24.6     295 

34.5 

39.4 

44.3 

49.2 

6 

43.3 

86.6 

31.5 

39.4     473 

55.1 

63.0 

70.9 

78.8 

36 

72.2 

26  3 

328     39.4 

45.9 

52.5 

59.1 

65.6 

• 

32.5 

64.9 

23.6 

29.5     35.4 

41.3 

47.3 

53.2 

59  1 

7 

50  5 

101.0 

36.8 

45.9     55  1 

64.3 

73.5 

82.7 

91.9 

42. 

84.2 

30  6 

38.3     45.9 

53.6 

61.3 

68.9 

76.6 

7 

37.9 

75.8 

27.6 

34.5     41  3 

48.2 

55.1 

62.0 

68  9 

8 

57.7 

115  4 

42.0 

52.5     63.0 

73.5 

84.0 

94.5 

105.0 

8 

48. 

96  2 

35.0 

43.8     52.5 

61.2 

70.0 

78.8 

87.5 

8 

43.3 

86.6 

31.5 

39.4     47.2 

55.1 

63  0 

70.9 

78.8 

9 

64.9 

129.9 

47.3 

59.1     70.9 

82.7 

94.5 

106.3 

118.1 

9 

54.1 

108.2 

39.4 

49.2     J9.1 

68.9 

78.8 

88.6 

98.4 

9 

48.7 

97.4 

35.4 

44.3     53.2 

62.0 

70.9 

79.7 

88.6 

10 

72.2 

144.3 

52.5 

65.6     "8.8 

91  9 

105.0 

118  1 

131.3 

10 

60.1 

120.3 

43.8 

54  .7     (is  6 

76  6 

87.5 

98.4 

109.4 

10 

54.1 

108.2 

39.4 

49.2     59.1 

08.9 

78.8 

88.6 

98.4 

SHOP   RIVETS 

FIELD   RIVETS 

BOLTS 

NO. 
OF 

SHEAR  AT 
11000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  22000  LBS./SQ.  IN. 

NO. 
OF 

SHEAR  AT 
9000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  18000  LBS./SQ.  IN. 

NO. 
OF 

SHEAR   AT 
8000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  16000  LBS./SQ.  IN. 

RIVS. 

SINGLE 

DOUBLE 

l 

4 

A      ! 

A 

1 

A 

! 

RIVS. 

SINGLE 

DOUBLE 

1 

A     i 

A 

i 

A 

1 

RIVS. 

SINGLE 

DOUBLE 

1 

4 

A      1 

A 

\ 

A 

1 

6.6 

13.2 

4.8 

6.0       7.2 

S.4 

9.6 

10.8 

12.0 

1 

5.4 

10.8 

3.9 

4.9       5.9 

6.9 

7.9 

8.9 

9.8 

1 

4.8 

9.6 

3.5 

44       53 

6.1 

70 

7.9 

8.8 

13.2 

26  5 

96 

120     14.4 

16.8 

19.3 

21.7 

24.1 

2 

10.8 

21.6 

7.9 

9.8     11.8 

13.8 

15.8 

17.7 

19.7 

2 

9.6 

19.2 

7.0 

8.8     10.5 

12.3 

14.0 

15.8 

17.5 

19.  8 

39.7 

14.4 

18.0     21.7 

25.3 

28.9 

32.5 

36.1 

3 

16.2 

32.5 

11.8 

14.8     17.7 

20.7 

23.6 

26.6 

29.5 

3 

14.4 

28.9 

10.5 

13  1     158 

18.4 

21.0 

23  6 

26  3 

26.5 

52  9 

19.2 

24.1     28.9 

33.7 

38.5 

43  3 

48.1 

4 

21.6 

43  3 

15.8 

19.7     23.6 

27.6 

31.5 

35.4 

39.4 

4 

19.2 

38.5 

14.0 

17.5     21.0 

24.5 

28.0 

31.5 

35  0 

33.1 

66  1 

24.1 

30.1     36.1 

42.1 

48.1 

54.1 

60.2 

S 

27.1 

54.1 

19.7 

24.6     29.5 

34.5 

39.4 

44.3 

49.2 

5 

24.1 

48.1 

17.5 

21.9     263 

30.6 

35.0 

39.4 

43  8 

6 

39.7 

79.4 

28.9 

36.1     43.3 

50.5 

57.8 

65.0 

72.2 

6 

32.5 

64.9 

23  6 

29.5     35.4 

41.3 

47.3 

53.2 

59.1 

6 

28.9 

57.7 

21.0 

26.3     31.5 

36.8 

42.0 

47.3 

52  5 

7 

46.3 

92.6 

33.7 

42.1     50.5 

59.0 

67.4 

75.8 

84.2 

7 

37.9 

75.8 

27.6 

34.5     41  3 

48.2 

55.1 

62.0 

68.9 

7 

33.7 

07.3 

24.5 

30.6     36.8 

42.9 

49.0 

55.1 

61  3 

8 

52.9 

105  8 

38.5 

48.1     57.8 

67.4 

77.0 

86.6 

96.2 

8 

43.3 

86.6 

31.5 

39.4     47.2 

55.1 

63  0 

70.9 

78.8 

8 

38.5 

77.0 

28.0 

35.0     42.0 

49.0 

56.0 

63  0 

70.0 

9 

59.5 

119.1 

43  3 

54.1     65.0 

75.8 

86.6 

97.5 

108.3 

9 

48.7 

97.4 

35.4 

44.3     53.2 

62.0 

70.9 

79.7 

88.6 

9 

43.3 

86.6 

31  5 

39.4     47.3 

55.1 

63.0 

70.9 

78.8 

10 

66  1 

132.3 

48  1 

(ill  2     72.2 

84.2 

•IS  3 

108.3 

120.3 

10 

54.1 

108.2 

39.4 

49.2     59.1 

68.9 

78.8 

88.6 

98.4 

10 

48.1 

96.2 

35  0 

43.8     52.5 

61  3 

70.0 

78.8 

87.5 

SHOP    RIVETS 

FIELD   RIVETS 

BOLTS 

NO. 
OF 

SHEAR   AT 
10000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  20000  LBS./SQ.  IN. 

NO. 

OF 

SHEAR  AT 
8000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  16000  LBS./SQ.  IN. 

NO. 
OF 

SHEAR   AT 
7000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  14000  LBS./SQ.  IN. 

RIVS. 

SINGLE 

DOUBLE 

1 

4 

A      t 

A 

J 

A 

1 

RIVS. 

SINGLE 

DOUBLE 

1 

4 

A         1 

A 

* 

ft 

1 

RIVS. 

SINGLE 

DOUBLE 

1 

4 

A     i 

A 

i 

ft 

1 

1 

6.0 

12.0 

4.4 

5.5       6.6 

7.7 

8.8 

9.8 

10.9 

4.8 

9.6 

3.5 

4.4       5.3 

6.1 

7.0 

7.9 

8.8 

1 

4.2 

8.4 

3.1 

38      4.6 

5.4 

6.1 

6.9 

7.7 

ilo 

24.1 

8.8 

10.9     13.1 

15.3 

17.5 

19.7 

21.9 

9.6 

19.2 

7.0 

8.8     10.5 

12.3 

14.0 

15.8 

17.5 

2 

8.4 

16.8 

6.1 

7.7       9.2 

10.7 

12.3 

13.8 

15.3 

18.0 

36.1 

13  1 

16.4     19.7 

23.0 

26.3 

29.5 

32.8 

14.4 

28.9 

10  5 

13  1     15.8 

18  4 

21.0 

23  6 

26  3 

12.6 

25  3 

9.2 

11.5     138 

16.1 

18.4 

L'O  7 

23.0 

24.1 

48.1 

17.5 

21.9     263 

30.6 

35.0 

39.4 

43.8 

19.2 

38.5 

14  0 

17.5     21.0 

24.5 

28.0 

31  5 

35.0 

16.8 

33.7 

12.3 

15.3'     18.4 

21.4 

24.5 

27.6 

30  6 

30.1 

60.1 

21.9 

27.3     32.8 

38.3 

43.8 

49.2 

54.7 

24.1 

48.1 

17.5 

21  9     263 

30.6 

35.0 

39.4 

43.8 

21.0 

42.1 

15.3 

19.1     23.0 

26.8 

30.6 

34.5 

38.3 

36.1 

72.2 

26.3 

32.8     39.4 

45.9 

52.5 

59.1 

65  6 

23.  9 

57.7 

21.0 

26.3     31.5 

36.8 

42.0 

47.3 

52.5 

25.3 

50.5 

18.4 

23.0     27.6 

32.2 

36  8 

41.3 

45.9 

42.1 

84.2 

30.6 

38.3     45.9 

53.6 

61.3 

68.9 

76.6 

33.7 

67.3 

24.5 

30.6     36.8 

42.9 

49.0 

55.1 

61.3 

29.5 

58.9 

21.4 

26.8     32.2 

37.5 

42.9 

48.2 

53  6 

48.1 

96.2 

35.0 

43.8     52.5 

61.2 

70.0 

78.8 

87.5 

8 

38.5 

77.0 

28.0 

35.0     42.0 

49  0 

56.0 

63.0 

70  0 

33.7 

67.3 

24.5 

30.6     368 

42  9 

49.0 

55.1 

61.2 

9 

54.1 

108.2 

39.4 

49.2     59.1 

68.9 

78.8 

88  6 

98.4 

9 

43  3             866 

31.5 

39.4     473 

55.1 

63.0 

70.9 

78.8 

9 

37.9 

75.8 

27.6 

345     41  3 

48  2 

55.1 

62  0 

68.9 

10 

60.1           120.3 

43.8 

54.7     65.6 

76.6 

87.5 

98.4   109.4 

10         48.1              96.2 

35  0 

43.8     52.5 

61.3 

70.0 

78.8 

87.5 

10 

42.1 

84.2 

30  6 

38.3     45.9 

53.6     61.3 

68.9 

76.6 

1"   RIVET   VALUES 


311 


SHEARING   AND   BEARING  VALUES   FOR   l"   RIVETS   IN   THOUSANDS  OF   POUNDS 

1       RIVETS                                              BEARING    VALUES    TO    THE    LEFT    OF    THE    DOTTED    LINES    ARE    LESS    THAN    THE    SINGLE    SHEAR    VALUES 
BEARING  VALUES  IN  PLATES  THICKER  THAN  THOSE  GIVEN  ARE  GREATER  THAN  THE  DOUBLE  SHEAR  VALUES 

SHOP    RIVETS 

FIELD   RIVETS 

BOLTS 

NO. 
OF 
RIVS 

SHEAR  AT 
13000  LBS./SQ.  IN 

BEARING  IN  PLATE  AT  24000  LBS./SQ.  IN. 

NO. 
OF 

RIVS. 

SHEAR  AT 
10000  LBS.'SQ.  IN 

BEARING  IN  PLATE  AT  20000  LBS./SQ.  IN. 

NO. 
OF 
RIVS. 

SHEAR  AT 
9000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  18000  LBS./SQ.  IN. 

SINGLE 

DOUBLE 

I  |  A 

1 

A 

1 

\l 

i 

SINGLE 

DOUBLE 

1     A 

J 

.A 

1 

H 

t 

SINGLE 

DOUBLE 

f     A 

i 

A 

! 

« 

3 

4 

1 
2 
3 
4 
5 

6 
7 
8 
9 
10 

9.4 
18  9 
28  3 
37.7 
47.1 

56  6 
66.0 
75.4 
84  8 
94.2 

18.9 
37.7 
56.6 
75.4 
94  3 

113.1 
132  0 
150  8 

169  7 
188.5 

9.0  I  10.5 
18.0  :  21  0 
27  0  131  5 
36.0  :  42  fl 
45.0  j  52  5 

54  0  ;  63  0 

63  0  ;  73.5 
72.0;  84  0 
81.0  !  94  5 
90.0  !105.0 

12.0 
24  0 
36.0 
48  0 
60  0 

72.0 
84.0. 
96.0 
108.0 
120.0 

13.5 
27  .0 
40  .5 
54  .0 
67  .5 

81  .0 

94  .5 
108    0 
121    .5 
35    0 

15  1) 
30  0 
45.0 
60  0 
75  0 

90.0 
105  0 
120  0 
135  0 
150  0 

16.5 
33  0 
49.5 
66  0 
82.5 

99  0 
115.5 
132  0 
148  5 
165  0 

18.0 
36.0 
54  0 
72  0 
90.0 

108.0 
126  0 
144  0 
162.0 
180  0 

1 
2 
3 
4 
5 

6 
7 
8 
9 
10 

7.9 
15.7 
23.6 
31.4 
39.3 

47.1 
55.0 
62  8 
70.7 
78.5 

15.7 
31.4 
47.1 
62.8 
78  5 

94  2 
110  0 
125  7 
141  4 
157.1 

7.5      8.8 
15.0     17  5 
225     263 
300     350 
37  5     43  8 

45.0     52.5 
525     613 
60.0     700 
67.5     78.8 
75.0     87.5 

10  0 
20.0 
30  0 
40  0 
50  0 

60.0 
70  0 
80  0 
90  0 
100.0 

11.3 
22.5 
33  8 
45.0 
56  3 

67  5 
78.8 
90  0 
101  3 
112  5 

12.5 
25.0 

37.5 
50  0 
62.5 

75.0 
87.5 
100  0 
112.5 
125.0 

13  8 
27.5 
41  3 
55  0 
68.8 

82.5 
96  3 
110  0 
123.8 
137.5 

15.0 
30  0 
45.0 
60.0 
75.0 

90.0 
105.0 
120.0 
135.0 
150.0 

1 
1 
3 

4 

a 

6 
7 
8 
» 
10 

7.1 
14.1 

21.2 
28.3 
35.3 

42.4 
49.5 
56.6 
63  6 
70.7 

14.1 

28.3 
42.4 
56.5 
70.7 

84.8 
99.0 
113.1 
127.2 
141  4 

6.8      7.9 
13.5     15.8 
20.3     236 
27.0     31  5 
338     39.4 

40.5     47.3 
47.3     55.1 
54.0     630 
60.8     70.9 

67.5     7S.8 

9.0 
18.0 
27.0 
36.0 
45.0 

54.0 
03.0 
72.0 
81.0 

90.  0 

10.1 
20  3 
30.4 
40.5 
50.6 

60.8 
70.9 
81.0 
91.1 
101  3 

11.3 
22  5 
33.8 
45.0 
56.3 

67.5 

78:8 

90.0 
101  3 
112.5 

12.4 
24.8 
37.1 
49.5 
61.9 

74  3 
86.6 
99.0 
111.4 
123.8 

13.5 
27.0 
40.5 
54  0 

67  5 

81  0 
94  5 
108  0 
121.5 

13.1  .0 

SHOP    RIVETS 

FIELD    RIVETS 

BOLTS 

NO. 
OF 
RIVS. 

SHEAR  AT 
11000  LBS./SQ.  IN 

BEARING  IN  PLATE  AT  22000  LBS./SQ.  IN. 

NO. 
OF 
RIVS 

SHEAR  AT 
9000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  18000  LBS./SQ.  IN. 

NO. 
OF 

RIVS. 

SHEAR  AT 
8000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  16000  LBS./SQ.  IN. 

SINGLE 

DOUBLE 

I      A 

i 

A 

1 

tt 

f 

SINGLE 

DOUBLE 

1         A 

i 

A 

1 

H 

1 

SINGLE 

DOUBLE 

1     A 

\ 

A 

! 

tt 

1 

1 
I 
3 
4 
I 

6 

7 
8 
9 
10 

8.6 
17  3 
25  9 
34.6 
43.2 

51.8 
60.5 
69  1 
77.8 
86.4 

17  3 
34.6 
51.8 
69  1 
86.4 

103.7 
121.0 
138.2 
155  5 
172.8 

8.3       9.6 
165     193 
248     289 
330     38.5 
41.3     48.1 

49.5     57.8 
57.8     67.4 
660     770 
74.3     86.6 
82  5     96.3 

11.0 
22.0 
33  0 
44.0 
55.0 

66.0 
77.0 
88.0 
99  0 
110.0 

12.4 
24.8 
37.1 
49.5 
61.9 

74.3 

86.6 
99.0 
111  4 
123  8 

13.8 
27.5 
41.3 
55.0 
68.8 

82.5 
96  3 
110.0 
123  8 
137  5 

15  1 
30  3 
45  4 
60  5 
75.6 

90.8 
105.9 
121  0 
136  1 
51  3 

16  5 
33  0 
49  5 
66  0 
82.5 

99.0 
115  5 
132.0 
148  5 

165  It 

1 
2 
3 

4 

a 

6 

7 
8 
9 
1    10 

7.1 
14.1 

21  2 
28.3 
35.3 

42.4 

49.5 
56.6 
63  6 

7(1  7 

14  1 
28.3 
42.4 
56.5 
70.7 

84.8 
99.0 
113  1 
127.2 
141  4 

6.8       7.9 
135     158 
20.3     23  6 
27.0     31  5 
338     39.4 

40.5     473 
47.3     55.1 
540     630 
60  8     70.9 
67.5     78.8 

90 
18  0 
27.0 
36  0 
45.0 

54.0 
63  0 
72  0 
81.0 
90  0 

10.1 
20  3 
30.4 
40.5 
50.6 

60  8 
70.9 
81.0 
91.1 
101.3 

11.3 

22  5 
33.8 
45  0 
56  3 

67  5 
78.8 
90.0 
101.3 

112  5 

12  4 
24.8 
37.1 
49.5 
61  9 

74  3 
86  6 
99.0 
111  4 

123.8 

13.5 
27.0 
40.5 
54  0 
67  5 

81.0 
94.5 
108.0 
121  5 
135  0 

1 
1 
3 

4 
1 

6 
7 
8 
9 
10 

6.3 
12.6 
18.8 
25.1 
31.4 

37.7 
44.0 
50.3 
56.5 
62.8 

12.6 
25.1 
37.7 
50.3 
62.8 

75.4 

88.0 
100.5 
113  1 

125.7 

6.0      7.0 
12.0     14.0 
18.0     21.0 
24.0     28.0 
300     350 

36.0     42.0 
42.0     49.0 
480     560 
54.0     63.0 
60.0     70.0 

8.0 
16.0 
24.0 
32.0 
40.0 

48.0 
56.0 
64  0 
72.0 
80.0 

9.0 
18.0 
27.0 
36.0 
45.0 

54.0 
63.0 
72.0 
81.0 
90.0 

10.0 
20.0 
30.0 
40.0 
50.0 

60.0 
70.0 
80.0 
90.0 
100.0 

11.0 
22.0 
33.0 
44.0 
55.0 

66.0 
77.0 
88.0 
99.0 
110.0 

12.0 
24  0 
36.0 
48  0 
60  0 

72.0 
84.0 
96.0 
108  0 
120.0 

SHOP   RIVETS 

FIELD    RIVETS 

BOLTS 

NO. 
OF 
RIVS. 

SHEAR  AT 
10000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  20000  LBS./SQ.  IN. 

NO. 
OF 

RIVS. 

SHEAR  AT 
8000  LBS    SQ    IN 

BEARING  IN  PLATE  AT  16000  LBS./SQ.  IN. 

NO. 
OF 

RIVS. 

SHEAR  AT 
7000  LBS./SQ.  IN. 

BEARING  IN  PLATE  AT  14000  LBS./SQ.  IN. 

SINGLE 

DOUBLE 

i     A 

i 

A 

f 

« 

t 

SINGLE 

DOUBLE 

1        A 

i 

A 

t 

« 

f 

SINGLE 

DOUBLE 

1         A 

i 

A 

1 

H 

i 

1 

2 

3 

! 

,• 

7.9 
15.7 
23  6 
31.4 
39.3 

47  1 
55  0 
62.8 
70.7 
78  5 

15.7 
31.4 
47.1 

62  8 
78.5 

94.2 
110  0 
125  7 
141  4 
157  1 

7.5      8.8 
15.0     175 
225     263 
30  0     35  0 
375     438 

450     525 
525     61  3 
600     700 
67.5     788 
75  0     87  5 

10  0 
20.0 
30  0 
40  0 
50  0 

60  0 
70  0 
80  0 
90  0 
100  0 

11  3 

22  5 
33  8 
45  0 
56  3 

67.5 
78.8 
90.0 
101  3 
112.5 

12.5 
25  0 
37.5 
50  0 
62.5 

75.0 
87  5 
100  0 
112  5 
125  0 

13.8 
27  5 
41  3 
55  0 

68.8 

82.5 
96  3 
110.0 
123.8 
137.5 

15  0 
30  0 
45  0 
60  0 
75  0 

90  0 
105  0 
120  0 
135  0 
150  0 

6 

7 
8 
9 
10 

6.3 
12  6 
18  8 
25.1 
31  4 

37.7 
44  0 
50  3 
56  5 
62  8 

12  6 
25  1 
37.7 
50  3 
62.8 

75  4 
88.0 
100.5 
113  1 
125  7 

60       7.0 
12  0     14  0 
180     21  0 
240     280 
300     350 

36  0     42  0 
420     490 
480     560 
54  0     63  0 
60.0     700 

8.0 
16  0 
24.0 
32  0 
40  0 

48  0 
56  0 
64  0 
72.0 
80  0 

9.0 
18.0 
27  0 
36  0 
45  0 

54  0 
63  0 
72  0 
81.0 
90.0 

10.0 
20.0 
30  0 
40  0 
50  0 

60  0 
70  0 
80  0 
90  0 
100  0 

11.0 
22.0 
33  0 
44  0 
55  0 

66  0 
77  0 
88.0 
99.0 
10.0 

12.0 
24.0 
36  0 
48.0 
60  0 

72.0 
84  0 
96  0 
108.0 
20.0 

1 

a 

3 
4 

I 

6 
7 
8 
9 
10 

5.5 
11.0 
16  5 
22  0 

27.5 

33  0 
38.5 
44.0 
49  5 
55.0 

11.0 
22.0 
33  0 
44  0 
55.0 

66  0 
77.0 
88  0 
99.0 
110  0 

53       61 
105      12  3 
158     18.4 
21.0     24.5 
263     30.6 

315     368 
36  8     42.9 
42.0     49.0 
47  3     55  1 
525     613 

7.0 
14.0 
21.0 
28.0 
35  0 

42  0 
49  0 
56  0 
63  0 
70  0 

79 
15  8 
23.6 
31.5 
39  4 

47.3 
55  1 
63  0 
70.9 
78.8 

8.8 
17.5 
26.3 
35.0 
43.8 

52.5 
61  3 
70  0 

78.8 
87  5 

96 
19  3 
28  9 
38  5 
48.1 

57.8 
67.4 
77.0 
86  6 
96  3 

10.5 

21.0 
31  5 
42  0 
52.5 

63  0 
73  5 
84  0 
94  5 
105  0 

312 

o 


GRAPHIC  RESULTANTS-DECIMALS 

6  7  8  9  10  If 


13 


14 


15 


ie 


13 


14 


16 


If 


313 


GRAPHIC  RESULTANTS-INCHES  AND  FRACTIONS 


314 


GRAPHIC  RESULTANTS -FEET  AND  INCHES 

6  7  8  9  .10  II  12 


Ifflfflflffllffi 


10  II  12  13 


315 


PURLIN  CONNECTIONS,  LATTICE   BARS,  AND  RODS  (AMERICAN  BRIDGE  COMPANY) 


PURLIN  CONNECTIONS 


LATTICE  BARS 


AREAS  AND  WEIGHTS  OF  RODS 


Purlin  connections  srs  usually  boltej 


ANGLE  PURLINS 


2i  x  21 
8x21 
3x21 

31x21 


DIAM. 
IN. 


Single  Lattice 


MAXIMUM   DISTANCE 


IT 

Ordinary  Connection 


Use  fhnge  connection  with  web 
connection  for  8,  9,  and  10  inch 
channels  and  for  6  inch  Z-Bars, 
Omit  flange  connection  for 
smaller  sections. 


Purlin  connections  are  usually  bolted 


CHANNEL  AND 
Z-BAR   PURLIN 


10 


3x21 
Six  21 
4x3 
4x3 
4x3 
5x31 
5x3i 


e  flange  connection  instead 
of  web  connection  for  l-Beama 
8  inches  or  over, 


Ordinary  Connections 
Ati  4    2ilt 


Pur'in  connections  are  usually  bolted 


I-BEAM   PURLINS 


4x3 
4x3 
5x34 


Strut  Connections 


THICKNESS  t 


1'IOJ" 


1'Oi" 
10" 


2'7i" 


cr 

3f" 

'Oi" 


Double  Lattice 


MAXIMUM   DISTANCE  c' 


THICKNESS; 


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2'9|" 

2'6" 

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1'IOJ" 


1 

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1.77 

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2.76 

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3.55 
3.98 
4.43 


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2.7 
3.4 
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DIAGRAM  FOR  BEARING  PLATES 

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1 

RAILS.  RAIL   FASTENINGS.  AND  UNIT  STRESSES  FOR  STEEL 


317 


DIMENSIONS  AND  PROPERTIES  OF  RAILS 

UNIT  STRESSES  FOR  STRUCTURAL  STEEL 
POUNDS  PER  SQUARE  INCH 
RECOMMENDED  BY  THE  AMERICAN  RAILWAY  ENGINEERING  ASSOCIATION 

STAND- 
ARD 

SKETCH 

WEIGHT 

AREA 

SECTION|  DEpTH 
MODULUS    UL 

FLANGE 

FLANGE 

HEAD 

HEAD 

WEB 

GAGE 

SPLICE 

BARS 

POUNDS 
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N   NET  SECTION. 
XIMUM  VALUE  OF   14.000     AXIAL  COMPRESSION. 
N.  WHERE   I   IS  THE  LENGTH  OF  THE  MEMBER 
IS  THE   LEAST  RADIUS  OF  GYRATION. 

S1ON.  ON  STEEL  CASTINGS. 

REME  FIBERS  OF  ROLLED  SHAPES. 
GIRDERS.  AND  STEEL  CASTINGS-NET  SECTION. 
•REME  FIBERS  OF  PINS. 

NS  AND  SHOP  DRIVEN  RIVETS. 
JRNED  BOLTS  AND  FIELD  DRIVEN   RIVETS. 
ATE  GIRDER  WEBS-GROSS  SECTION. 

S  AND  SHOP  DRIVEN  RIVETS. 
RNED  BOLTS  AND  FIELD  DRIVEN   RIVETS. 
ONRY. 
ANSION  ROLLERS  PER  LINEAL 
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( 

2-0  to  2-6" 

Ld'to    I'-e" 



I 

318 


SHEAR  AND  MOMENT  TABLE  FOR  COOPER'S  E60  LOADING. 


ALL  LOADS,  SHEARS,  AND   MOMENTS  ARE  FOR  EACH  RAIL.  HORIZONTAL  DISTANCES  ARE  PLOTTED  TO  THE  SCALE  1  IN.  =  16  FT. 
THE  VALUES  GIVEN  IN  THE  TABLE  ARE  FOR  COOPER'S  CONVENTIONAL  E60  LOADING.    VALUES  FOR  COOPER'S  OTHER  LOADINGS 
MAY  BE  OBTAINED  FROM  THOSE  IN  THE  TABLE  BY  PROPORTION,  AS  FIVE-SIXTHS  FOR  E50,  OR  TWO-THIRDS  FOR  E40. 
FIRST  ENGINE                                                                                               SECOND  ENGINE                                                TRA|N 

PILOT                                DRIVERS                                                          TENDER                                PILOT                                 DRIVERS                                                         TENDER                           UNIFORM    LOAD 

1                                                           II                                                          i                                    1                                                           II                                                   1 
30.0          30.0           30.0          30.0                                                                                                                               30.0          30.0          30.0           30.0 

WHEEL  LOADS  OH  EACH   RAIL.™               (O|   ^   ^   ^1                 A      A         A      A                ^                f^S  f5S   ^  I^S                 ^       A         ^       £> 

,N  THOUSANDS  OF  POUNDS  CD     vA'A'Av      GO  (0   CO  CO      c^D      v'Avv  Av      £L@_j£L@ 

3.0  PER    LIN.  FT. 

^^^^^ 

DIST.  C.  TO  C.  WHEELS  IN   FEET 

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DISTANCES  TO  THE  CENTERSL 

w 

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2.4 

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OF    GRAVITY    OF    DIFFERENT 
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EST LOADS. 

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->[;£      FIRST  LINE  AT  THE  LEFT 
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SHEARS 
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11GHT     OF     ANY 
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S.  OF  THE  LOAD 
"LY  OVER  THIS 
AL.  OF  THE  LOAD 
•HE  FIRST    LINE 
:  RIGHT  OF  THE 
AND     OF     ALL 
BETWEEN  THESE 

S       420 

g    411 

5  381 

§  351 

5        321 

R  291 

£     27/5 

S2S2 

§      232? 

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^.198 

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S          108 

S  78 

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w39 

THE 
VERTIC 
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VERTIC 
OVER  1 
AT  THI 
VALUE 
LOADS 
TWO. 

§      406.5 

3   391? 

a,  36/? 

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^  27  If 

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§232,5 

3       2/3 

?.       193? 

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to  39 

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2       387 

S  372 

3,342 

R  3/2 

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S2S2 

g    232.5 

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!?       193? 

£        174 

%I59 

^129 

S  9S 

2          69 

to  39 

39   to 

58.5 

§S       367,5 

§  352? 

K  322s 

5  292.5 

£        262.5 

§  232.5 

5     2/3 

$  193? 

%        174 

%        154? 

3,139? 

ZI09.5 

Z  79f 

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39w 

SS.s; 

78  S 

?i       348 

^  333 

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3273 

§        243 

£  2/3 

S     193? 

§  174 

S5       154? 

Z        135 

5/20 

^  90 

•o  60 

49.5  o> 

695 

88.^ 

108  $ 

Si       318 

8  303 

3273 

§243 

3        2/3 

^  183 

^     163? 

^144 

§       124? 

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118?$ 

138  £ 

§       288 

3  273 

Eg  243 

B  2/3 

§        183 

£  153 

£     /33.5 

%  H4 

Si         94? 

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§  243 

5  2/3 

£  183 

?        153 

55  123 

Si     103? 

^    84 

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2/3  « 

MOMENTS 
EACH  VERTICAL  OF  THE  ZIG- 
ZAG  LINE  CONTAINS  THE  POINT 
OF   MOMENTS  FOR  ALL  VALUES 

24,500 

22,900 

19,900 

17,000 

14,300 

11:700 

10,200 

8,790 

7,500 

6,310 

5,510 

4,160 

2,960 

1,910 

1,010 

605 

293 

97.5 

MOMENTS 
EACH  VERTICAL 
E  ZIG-ZAG    LINE 
INS  THE    POINT 
HENTS    FOR  ALL 
S  ON  THE  RIGHT 
IS    LINE.    EACH 
IS  THE  MOMENT. 
OUSANDS     OF 
•FEET.   OF  ALL 
FROM  THE  POINT 
MENTS   TO    AND 
>ING  THE  LOAD 
fHE  FIRST  LINE 
RIGHT  OF  THE 

22,400 

20,900 

18,000 

15,200 

12,700 

10,200 

<£,830 

7,530 

6,340 

5,240 

4,520 

3,320 

2,270 

1,370 

624 

312 

97,5 

OF  TH 
CONTA 
OF  MO 
VALUE 
OF    TH 
VALUE 
IN     TH 
POUNC 
LOADS 
OF    MO 
INCLUI 
OVER 
AT  THE 
VALUE 

20,400 

18,900 

16,200 

13,600 

11,200 

8,880 

7,570 

6,360 

5,270 

4,280 

3,630 

2,580 

1,680 

932 

332 

117 

97.5 

ON  THE  LEFT  OF  THIS  LINE.  EACH 
VALUE     IS     THE     MOMENT.     IN 
THOUSANDS    OF    POUND-FEET, 
OF  ALL  LOADS  FROM  THE  POINT 
OF  MOMENTSTO  AND  INCLUDING 
THE  LOAD  OVER  THE  FIRST  LINE 
AT  THE  LEFT  OF  THE  VALUE. 

18,100 

16,700 

14,100 

11,700 

9,470 

7,370 

6,180 

5,090 

4,1/0 

3,230 

2,0(0 

1,810 

1,090 

518 

97? 

117 

332 

16,200 

14,900 

12,500 

10,300 

8,150 

6,200 

5,110 

4,120 

3,240 

2,460 

1,980 

1,260 

690 

270 

97? 

312 

624 

13,100 

11,900 

9,780 

7,800 

5,970 

4,290 

3,370 

2,550 

1,850 

1,250 

900 

450 

/SO 

I/O 

449 

839 

1,330 

11,500 

10,400 

8,410 

6,580 

4,900 

3,370 

2,550 

1,830 

1,230 

720 

450 

150 

ISO 

423 

794 

1,280 

1,870 

10,100 

9,030 

7,200 

5,520 

3,990 

2,610 

1,890 

1,260 

755 

345 

150 

150 

450 

821 

1,290 

1,870 

2,560 

8,770 

7,810 

6,130 

4,600 

3,220 

1,990 

1,370 

842 

432 

120 

iso 

450 

900 

1,370 

1,930 

2,620 

3,400 

6,950 

6,110 

4,670 

3,380 

2,240 

1,250 

780 

410 

156 

240 

630 

1,170 

1,860 

2,480 

3,210 

4,040 

4,980 

PROPERTIES   OF    WOODEN    RECTANGULAR    BEAMS 


319 


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WORKING   UNIT  STRESSES   FOR   STRUCTURAL  TIMBER 

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RECOMMENDED  BY  THE  AMERICAN  RAILWAY  ENGINEERING  ASSOCIATION 
(EXCEPT  TWO  COLUMNS   "X") 
UNIT  STRESSES  ARE  FOR  GREEN  TIMBER  AND  SHOULD  BE   USED  WITHOUT 
INCREASING  THE  LIVE  LOAD  STRESSES  FOR  IMPACT 

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3,430 
4.000 

4,631 
5,324 
6,084 
6,912 
7,813 

8,788 
9,842 
10,980 
12,190 
13,500 

0.5 
1.8 
4.3 
8.5 

14  6 
23.2 
34.7 
49.4 

67.7 

90.1 
117.0 
148.8 
185.8 
228.5 

277.3 
332.7 
394.9 
464.4 
541.7 

627.0 
721.0 
823.8 
936.0 
1,058 

,190 
,333 
,486 
,651 
,828 

2,219 
2,661 
3,159 
3,715 
4,333 

5,016 
5,768 
6,590 
7,488 
8,464 

9,520 
10,660 
11,890 
13,210 
14,620 

0.6 

2.0 
4.7 
9.1 

15.8 
25.0 
37.3 
53  2 
72.9 

97  1 
126.0 
160.2 
200  1 
246.1 

298.7 
358.2 
425  3 
500.1 
583.3 

675.3 
776.4 
887.2 
1,008 
1,139 

1,282 
1,435 
1,601 
1,778 
1,969 

2,389 
2,866 
3,402 
4,001 
4,667 

5,402 
6,211 
7,097 
8,064 
9,115 

10,250 
11,480 
12,810 
14,230 
15,750 

0.6 

21 
5.0 
9.8 

16  9 
26  8 
40.0 
57.0 

78.1 

104.0 

135  0 
171  6 
214  4 
263.7 

320.0 
383  8 
455.6 
535.9 
625.0 

723,5 
831.9 
950.6 
1,080 
1,221 

1*73 
1,538 
1,715 
1,905 
2,109 

2,560 
3,071 
3,645 
4,287 
5,000 

5,788 
6.655 
7,604 
8,640 
9.766 

10,990 
12,300 
13,720 
15,240 
16,880 

0.7 
2.3 
53 
10  4 

18.0 
28.6 
42.7 
60  8 
83.3 

110.9 
144.0 
183.1 
228.7 
281.3 

341  .3 
409.4 
486.0 
571.6 
666.7 

771.8 
887.3 
1,014 
1,152 
1,302 

1,465 
1,640 
1,829 
2,032 
2,250 

2,731 
3,275 
3,888 
4.573 
5,333 

6,174 
7,099 
8,111 
9,216 
10,420 

11,720 
13,120 
14,630 
16,260 
18,000 

RAILWAY  BRIDGES  AND 
TRESTLES 

DOUGLAS  FIR  
LONGLEAF  PINE  
SHORTLEAF  PINE    . 

1200 
1300 
1000 
900 
1100 
800 

1100 
850 
700 
800 
1100 

1200 
1300 
1100 
900 
1000 
800 
900 
1100 
900 
900 
800 
1100 

i.siVooo 

1,610,000 
1.480,000 
1,130,000 
1,310,1X10 
1,190,000 
1,220,000 
1,480,000 
800,000 
1,150,000 
860,000 
1,150,000 

1000 
1300 
1100 
500 
1000 

1100 

450 
1000 

170 
180 
170 

too 

150 
130 
170 
160 
80 
120 

110 
120 
130 
70 
70 
100 
100 
100 

310 
260 
170 
150 
180 
150 
220 
220 
150 
170 
230 
450 

1200 
1300 
1100 
1000 
1100 
800 
1000 
1200 
900 
1100 
900 
1300 

900 
980 
830 
750 
830 
600 
750 
900 
680 
830 
680 
980 

1200(1-2/60(2) 

i30oa-2/60i2) 

1100(1-2/60/2) 
1000(1-2/60(2) 
1100(1-2/60(2) 
800(1-2/60(2) 
1000(1-2/60(2) 
1200(l-!/60rf) 
900(1-2/60(1) 
1100(1-2/60(0 
900(1  -2/60  (2) 
1300  (1-2/60  (2) 

WHITE  PINE  

SPRUCE 

NORWAY  PINE 

TAMARACK  
WESTERN   HEMLOCK.. 
REDWOOD               

BALD  CYPRESS  
RED  CEDAR  
WHITE  OAK  

210 

110 

HIGHWAY  BRIDGES  AND 
TRESTLES 

DOUGLAS  FIR 

1500 
1630 
1250 
1130 
1380 
1000 

1500 
1630 
1380 
1130 
1250 
1000 
1130 
1380 
1130 
1130 
1000 
1380 

1,510,000 
1,610,000 
1,480,000 
1,130,000 
1,310,000 
1,190,000 
1,220,000 
1,480,000 
800,000 
1,150,000 
860,000 
1,150,000 

1250 
1630 
1380 
630 
1250 

1380 

560 
1250 

210 
230 
210 
125 
190 
160 
210 
200 
100 
150 

260 

140 
150 
160 
90 
90 
125 
125 
125 

140 

390 
330 
210 
190 
230 
190 
280 
280 
190 
210 
290 
560 

1500 
1630 
1380 
1250 
1380 
1000 
1250 
1500 
1130 
1380 
1130 
1030 

1130 
1230 
1030 
940 
1030 
750 
940 
1130 
850 
1030 
850 
230 

1500(1-2/60(2) 
1630  (l-2/60(?) 
1380  (1-2/60(2) 
1250(1-2/60(2) 
1380(1-2/60(2) 
1000(1-2/60(2) 
1250(1-2/60(2) 
1500(1-2/60(2) 
1130(1-2/60(2) 
1380(1-2/60(2) 
1130(1-2/60(2) 
1630(1-2/60(2) 

LONGLEAF  PINE    . 

SHORTLEAF  PINE  
WHITE  PINE  

SPRUCE 

NORWAY  PINE      ...     . 

TAMARACK  

WESTERN  HEMLOCK.. 
REDWOOD  

1380 
1060 
880 
1000 
1380 

BALD  CYPRESS  

RED  CEDAR  

WHITE  OAK  

BUILDINGS  AND  SIMILAR 
STRUCTURES  FREE  FROM 
IMPACT  AND  EXPOSURE 

DOUGLAS  FIR  .. 

1800 
1950 
1500 
1350 
1650 
1200 

1650 
1280 
1050 
1200 
1650 

1800 
1950 
IMO 
1350 
1500 
1200 
1350 
1650 
1350 
1350 
1200 
1650 

755,000 
805,000 
740,000 
565,000 
655,000 
595,000 
61(1,000 
740,000 
400,000 
575,000 
430,000 
575,000 

1500 
1950 
1650 
750 
1500 

1650 

680 
1500 

260 
270 
260 
150 
230 
200 
260 
240 
120 
180 

170 
180 
200 
110 
110 
150 
150 
150 

470 
39J 
260 
230 
270 
230 
330 
330 
230 
260 
350 
680 

1800 
1950 
1650 
1500 
1650 
1200 
1500 
1800 
1350 
1650 
1350 
1950 

1350 
1470 
1250 
1130 
1250 
900 
1130 
350 
1020 
250 
1020 
1470 

1800(1-2/60(2) 
1050(1-2/60(2) 
1650(1-2/60(2) 
1500(1-2/60(2) 
1650(1-2/60(2) 
1200(1-2/60(2) 
1500(1-2/60(0 
1800(1-2/60(2) 
1350(1-2/60(2) 
1650(1-2/60(2) 
1350(1-2/60(2) 
1950(1-2/60(2) 

LONGLEAF  PINE  
SHORTLEAF  PINE  

WHITE  PiNE 

SPRUCE  

NORWAY  PINE   

TAMARACK  
WESTERN  HEMLOCK.. 
REDWOOD  
BALD  CYPRESS  
RED  CEDAR 

WHITE  OAK  

320 

170 

*  USE  THE  VALUES  OF  "E"  GIVEN  IN  THE  BOTTOM  TABLE  FOR  FINDING  THE  DEFLECTION 
OF    BEAMS    UNDER    QUIESCENT   OR    LONG    CONTINUED    LOADS.     USE    THE    VALUES    IN   THE 
UPPER  TABLES  WHEN  THE   LOADS  ARE   SUDDENLY  APPLIED 

7113 
'875 

AREAS   AND   WEIGHTS   OF    PLATES 


321 


AREAS  OF  PLATES  IN   SQUARE  INCHES 

WEIGHTS  OF 

PLATES   IN   POUNDS   PER   LINEAL  FOOT" 

IDTH 
IN 
NS. 

THICKNESS  IN  INCHES 

WIDTH 
IN 
INS. 

THICKNESS  IN  INCHES 

i 

A 

I 
8 

If 

* 

A   1    1    1  tt       I       ffil 

H 

1 

*A|  *i 

1  Hi 

l£ 

Iff 

»t 

*A 

o 

lA 

*t 

If* 

If 

If* 

1* 

It* 

2 

t 

/I, 

i 

A 

i 

A 

1 

a 

1 

i* 

i 

H 

1 

3 

075 

014 

1  13 

131 

1  50 

1.69!  1.88  2.06 

7  75 

2.44   2.63 

2.81   3.00 

3  19 

338 

3  .56 

375 

3  '14 

4  13 

431 

4  511 

489 

4.88 

.5  06 

5  1,5 

5,44 

,1.68 

5.81 

6.00 

1 

0.9 

I.I 

1.3 

I..5 

1.7 

1.9 

2.1 

2.3 

2.6 

2.8 

3.0 

3.2 

3.4 

4 

1.00 

1.25 

1.50 

1.75 

2.00 

2.25  2.50  2.75 

3.00 

3.25  3.50 

3.75'  4.00 

4,25 

4.50 

4,75 

5.00 

5.25 

550 

575 

600 

6.25 

6.50 

6.75 

7.00 

7.25 

7.50 

7.75 

8.00 

2 

1.7 

2.1 

2.6 

1.0 

3.4 

5.8 

4.3 

4.7 

5.1 

5.5 

6.0 

6.4 

6.8 

5 

1,25 

1,56 

1,88 

2,19 

2.50 

2.81  3.13 

3,44 

375 

406 

438 

t  61) 

500 

531 

5  63 

.51)4 

625 

656 

6SS 

719 

750 

7,81 

8.13 

8.44 

8.75 

11.06 

9.38 

11.611 

10.00 

3 

2.6 

3.2 

S.8 

4.  .5 

5.1 

5.7 

6.4 

7.0 

7.7 

8.3 

8.9 

9.6 

10.2 

6 

1.50 

1.88 

2.25 

2.63 

3.00 

3.38  3.75 

4.13 

4.50 

4.88 

5.25 

5.63 

6.00 

6.38 

6.75 

7.13 

7.50 

7.88 

8.25 

8.63 

9.00 

9.38 

9.75 

10.13 

10.50 

10.SS 

11.25 

11.63 

12.00 

4 

3.4 

4.3 

S.I 

6.0 

6.8 

7.7 

8.5 

9.4 

10.2 

11.1 

11.9 

12.8 

13.6 

7 

1  75 

2  19 

2.63 

3.06 

3.50 

3.941  4.38  4.81 

5.25 

589 

613 

656 

7,00 

7,44 

7.88 

8.31 

875 

9.19 

163 

10.0610.50 

10.94 

11.3811.81 

13.31 

2.69 

13.13 

13.56 

14.00 

5 

4.3 

£.3 

6.4 

7.4 

8.5 

9.6 

10.6 

11.7 

12.8 

13.8 

14.9 

159 

17.0 

8 

2.00 

2.50 

3.00  3.50 

4.00 

4.50  5.00J  5.50 

6.0C 

6.50 

7.00 

7.50 

8.00 

8.50 

9.00 

9.50  10.00 

IO.SO'11.00  11.50  12.00 

12.50  13.00  13.50  14.00 

.4.50   15.00   15.50 

16.00 

6 

5.1 

6.4 

7.7 

S.I) 

10.2 

11.5 

12.8 

14.0 

15.3 

16.6 

17.9 

111.1 

20.4 

9 

2  25 

281 

8.38 

3.94 

4.5(1 

5.06  5.63   6.19 

6.75 

7.31 

7.88 

8,44 

9.00 

9.56 

10.13 

.0.61H1.2.5 

1  ,81 

12.88 

12114 

13,5(1 

.4.06 

14.63 

15.19 

15.75 

16.81   16.88 

17.44 

18.00 

7 

6.0 

7.4 

8.1) 

111.4 

11.9 

13.4 

14.9 

lrt.4 

17.9 

19.3 

20.8  22.3 

23.8 

10 

2.50 

3.13 

3.75 

4.38 

5.00 

5.63 

6.25 

6.88 

7.50 

8.13 

8.75 

9.38 

10.00 

.0.63 

11.25 

.1.8812.50 

13.13 

13.75 

14.38 

15.00 

.5.63116.25 

16.88 

17.50 

18.13 

18.75 

19.38 

20.00 

8 

e.s 

8.5 

10.2 

1  1.9 

13.6 

15.3 

17.0 

18.7 

20.4 

22.1 

23.8  25.5 

27.2 

101 

256 

3.20 

3.84 

4.48 

5.13 

5.77 

6.41 

7.0.5 

7.69 

8.33 

8.97 

9.61 

10.2.5 

0.811 

11.53 

2  17 

12.81 

13,45 

1409 

14.73 

15.38 

16.0216.66 

1730 

17.94 

18,58 

19.22 

19.86 

20.50 

9 

7.7 

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11.5 

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763 

3  28 

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8.53 

9,19 

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1,16 

11.81 

147 

13  13 

1378 

14.44 

15.09 

15  75 

841 

1706 

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9.03 

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21.00 

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10.612.8 

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18.38 

19.25 

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22.75  23.63i24.50 

25.38 

26.25 

27.13 

28.00 

24 

20.4 

25.5 

30.635.7 

40.8 

45.9 

51.0   56.1 

61.2 

66.3  71.4 

76.5 

81.6 

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3.56 

4.45 

5.34 

6.23 

7.13 

8.02 

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12.47 

13.36 

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6.34 

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15.6716.5917.5218.44 

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21.20 

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23.05 

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91.8 

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3.75 

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15.9416.8817.81 

18.75 

19.69 

20,63 

21.5622.50 

23.44i24.38  25.31  26.25 

27.19 

28.13 

29.06 

30.00J 

28 

23.829.8 

35.7 

41.7 

47.6 

53.6  59.5 

65.5 

71.4 

77.4 

83.3 

89.3 

95.2 

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3.81 

4.77 

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6.67 

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9.53 

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12.39J13.34  14.30 

15.25 

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17.16 

1811 

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21.9222.88 

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25.7326.69 

27.64 

28.59 

29.55 

30,50 

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24.730.8 

37.043.1 

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67.8 

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4.84 

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6.78 

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1.5.51 

16.47117.44 

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11.00 

12.00 

13.00  14.00  15.00 

16.00 

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21.0022.00 

23.00 

24.00 

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29.00 

30.00 

31.00  32.00 

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6,09 

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8.13 

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25.3926.4127.4228.44 

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31.48  32.50 

33 

28.1 

35.1 

42.1 

49.1 

58.1 

63.1 

70.1 

77.1 

84.2 

91.2 

98.2 

105.2!ll2.2 

Si 

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4.13 
4.19 
4.25 

5.16 
5.23 
5.31 

6.19 
6.28 
6.38 

7.22 
7.33 
7.44 

8.25 
8.38 
8.50 

9.28 
9.42 
9.56 

10.31 
10.47 
10.63 

11.34 
11.52 
11.69 

12.38 
12.56 
12.75 

13.41 

13.61 
13.81 

14.44 

14.66 
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15.47 
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16.50 
16.75 
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17.53 
17.80 
18.06 

18.56 
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19.5920.63 
19.89E0.94 
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21.6622.6923.72 
21.9823.03:24.08 
22  .31J23.38  24.44 

24.7.5 
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25.78  26.8l!27.84j28.88 
26.1727.2228.2729.31 
26.5627.6328.6929.75 

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30.81 

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57.8 
59.5 
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72.3 
74.4 
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86.7 
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108.4 
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14.63  15.75 

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20.  19  21.  38  22.56  23J5 

24.9426.13 

27.31  28.50 

29.6930.8832.0633.25 

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16.25  17.50  18.75j20.00 

21.25  22.50:23.7.V25.0fl 

26.2527.5028.7530.01 

31.2532.5033.7535.00 

36.25.  37.501  38.751  40.00 

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99.5 

107.7116.0 

124.3 

132.6 

11 

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40 

3 

14 

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7.19 
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8.63 
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10.06,11.50 
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26.5628.12     72 

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16 
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11.38 
11.81 
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13.00 
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14.63 
15.19 

15.75 
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16.25 
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22.7524.3826.00 
23.6325.3127.00 
24.50  26  25  28.00 
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27.6329.25     ''« 
28.61130.38     84 
29.7531.50'    90 
30.81,32.63     96 

19.50  24.38  29.25i34.13  39.00 
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22.50  28.13  33.75,39.38  45.00 
24.00  30.0036.0042.0048.00 

43.8848.7553.6358.50 
47.2552.5057.7563.00 
50.6356.2561.8867.50 
54.0060.0066.0072.00 

63.38 
68.25 
73.13 
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68.25 
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73.13 
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78.00 
84.00 
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45 
46 
47 
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38.347.857.466.9 
39.148.958.768.4 
40.049.959.9169.9 
40.851.0161.271.4 

76.5 
78.2 
79.9 
81.6 

86.1 
88.0 
89.9 
91.8 

95.6105.2 
97.8107.5 
99.9  109.9 
102.0112.2 

114.8 
117.3 

119.1 
122.4 

124.3  133.9 
127.1  136.9 
129.8  139.8 
132.6  142.8 

143.4153.0 
146.6;156.4 
149.8159.8 
153.0:163.2 

10 

12 
14 
6 

7.50 
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9.38 
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11.2513.1315.00 

12.0014.0016.00 
12.75114.8817.00 
13.50  15.75  18.00 

16.88 
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70  ?5 

18.7520.6322.50 
20.0022.0024.00 
21.  25|23.38  2.5.50 
22.50l24.75l27.00 

24.3826.2528.1330.00 

26.0028.0030.0032.00 
27.63:29.7531.8834.00 
29.2531.50,33.75:36.00 

31.8833.75 
34.0036.00 
36.13|38.25 
38.2.5,40.50 

102  :25.50  31.8838.2544.6351.00 
108  27.00  33.7540.50,47.2554.00 
114  28.50  35.6342.7549.88:57.00 
120  30.00  37.50  45.00  52.50'60.00 

57.3863.7570.1376.50 
60.7567.5074.2581.00 
64.13:71.2578.38,85.50 
67.50:75.00.82.50:90.00 

S2.8S   S'J.2.- 
87.75  94.50 
92.63  99.7E 
97.50  105.0C 

95.63  102.00 
101.25  108.00 
106.88114.00 
112.50120.00 

49 

50 
51 
52 

41.7 

42.: 

43.4 
44.2 

52.162.572.9 
53.163.874.4 
,54.265.075.9 
55.366.377.4 

83.3 
85.0 
86.7 

884 

93.7104.1 
95.6  106.3 

97.5108.4 
99.5110.5 

114.5125.0 
116.9127.5 
119.2130.1 
121.6:132.6 

135.4 

138.1 
140.S 

143.: 

145.8 

148.8 
1.51.7 
1.54.7 

156.2  166.6 
159.4170.0 
162.6173.4 
165.8176.8 

8 

9.50 

11.88 

14.25  16.63  19.00 

21.38 

23.75 

26.1328.50 

30.8833.2535.63!.3S.OO 

40.3842.75              WEIGHTS  OF  PLATES   IN   POUNDS 

PER    LINEAL   FOOT* 

53 

45.156.367.6.78.8  90.1 

101.4112.6123.9135.2 

146.4'l57.7  168.9  180.2 

a    ao.oc 

12.S 

15.00  17.50120.CK 

22.51  '25.00  27.50  30.01 

32.50  35.« 

37.50  40.0( 

42.50  45.00 

1 

5 

I 

7 

l 

tt 

1 

I  11 

13 

I 

a 

1 

54 

45.9  57.4  68.S 

,80.3   91.1 

103.3114.8126.2137.7 

149.2  160.7 

172.1I83.B 

2 
4 

6 

8 

a 

2 

10.50 
11.00 
11.50 

12.00 
12.50 
13.00 

13.13 

13.75 
14.38 
15.00 
15.63 
16.25 

15.7.518.38 
16.5019.2S 
17.2520.13 
18.OOl21.OC 
18.75l21.86 
19.50'22.7c 

21.00 
22.00 
23.00 
24.00 
25.00 
26.(X 

23.63 

21.75 
25.8S 
27.01 
28.13 
29.25 

A.  2: 
27.50 
28.7.5 
30.00 
31.25 
32.50 

28.8831.50 
30.2533.00 
31.6334.50 
33.0036.00 
34.3837.50 
35.7539.00 

34.13|36.7539.38 
35.7538.5041.25 
37.3840.2543.13 
39.0042.0045.00 
40.63-43.75  46.88 
42.25:45.50:48.75 

42.00 
44.00 
46.00 
48.00 
50.00 
52.00 

43.63,47.25 
46.75.49.50 
48.8851.75 
51.00!54.00 
53.1356.25 
55.2558.50 

70.1 
76.5 
82.9 
89.3 
95.C 
102.0 

~84l2 
91.8 
99.5 
107.1 
114.8 
122.4 

126.2114(U|15C3|i68J 
137.7  153.o!l68.3^lS3.6 
149.2  165.8  182.3:198.9 
160.7178.5196.4214.2 
172.1191.3210.4,229.5 
183  6  'ni  n  i?-4  d'''-!*  fi 

55 
56 
57 
58 
59 
60 

46.S.5S.4 
47.659.5 
48.5  60.6 
49.361.6 
50.2  62.7 
51.063.8 

70.181.8   93.5 
71.483.3  95.2 
72.784.8  96.9 
74.086.3  98.6 
75.287.8100.3 
76.5,89.3  102.0 

105.2116.9128.6140.3 
107.1119.0130.9142.8 
109.0  121.  l!l33.2  145.4 
110.9  123.3'135.6'147.9 
112.8125.4137.9150.5 
114.8  127.5  140.3  153.0 

151.9,163.6175.3 
154.7166.6178.5 
157.5169.6181.7 
160.2:172.6,184.9 
163.o:i75.5  188.1 
165.8178.5191.3 

187.0 
190.4 
193.8 
197.2 
200.6 
204.0 

66 
72 
78 

84 
i    90 

93 

56.1 
61.2 
66.3 
71.4 
76.5 
81  6 

98.2 
107.1 
116.0 
125.0 
133.9 
1428 

112.2 
122.4 
132.6 
142.8 
153.0 
163  i 

182.3  11)6.4 
198.9214.2 
215.5232.1 
232.1  '249.9 
248.6,267.8 
165  2^285  6 

210.4 
229.5 
248.6 
267.8 
286.9 
3060 

224.4 
244.8 
265.2 
285.6 
306.0 
3264 

4 

S 

13.50 
14,00 

16.8820.2523.6327.00 
17.5021.0024.5028.00 

30.38'33.75  37.13  40.50 
31.5035.0038.5042.00 

43.8847.2550.6354.00 
45.50  49.0052.50  56.00 

57.3860.75,  102 
59.5063.00  1  108 

86.7168.4130.1151.1 
91.8  114.7  137.8  160.7 

173.4 
1837 

195.1 
206.6 

216.7238.4260.2 
229.5  -'.52.4:275.5 

281.8  303.5 
298.3  321.3 

(2.5.1 
344.3 

346.8 
367.2 

61 
62 

51.964.8 
52.765.9 

77.890.7  103.7 
79.192.2105.4 

116.7129.6142.6155.6 
118.6131.8144.9158.1 

168.5  181.5  194.4 
m.3'184.5  197.C 

207.4 
210.8 

t 

9 

14.50 
15.00 

18.1321.7525.3829.00 
18.75i22.50  26.25:30.00 

32.6336.2539.88,43.50 
33.7537.50:41.25!45.00 

47.1350.7554.3858.00 
48.7552.5056.25'60.00 

61.  6365.2? 
63.7567.50 

114    96.9  121.1  145.4  169.6  193.8 
120  102.0J12Z.5J153.0I178.5J204.0 

218.1I242.2266.4J290.8 
229.5255.0280.5306.0 

314.9339.2 
331.5J357.0 

363.4  387.6 
382.5  408.0 

63 
64 

53.666.980.393.7107.1 
54.416S.OJ81.695.2W8.8 

120.5  133.9:147.3  160.7 
122.4136.0149.6183.2 

174.0187.4200.8214.2 
176.8190.4204.0217.6 

*  WEIGHT  =  3. 4X  AREA,    OR    12  .CUBIC    INCHES    OF    STEEL    WEIGHS    3.4    POUNDS 


322 


PROPERTIES   OF    I-BEAMS 


IF  THE  THICKNESS  OF  THE  WEB  IS  MORE  THAN  gj  BELOW  AN  EVEN  SIXTEENTH.  THE                                     ^ 
NEXT  LOWER  SIXTEENTH  IS  GIVEN  IN  THE  TABLE  BELOW                                                       ^P" 

/=THE  MOMENT  OF  INERTIA  OF  THE  CROSS  SECTION  ABOUT  THE  AXIS  1-1 
«=THE  CORRESPONDING  SECTION  MODULUS  ABOUT  THE  AXIS  1-1 
r  =  THE  CORRESPONDING  RADIUS  OF  GYRATION  ABOUT  THE  AXIS  1-1 
A  =  THE  MOMENT  OF  INERTIA  OF  THE  CROSS  SECTION  ABOUT  THE  AXIS  2-2                                    •=={=> 
TS=THE  CORRESPONDING  RADIUS  OF  GYRATION  ABOUT  THE  AXIS  2-2                                                    2 

CARNEGIE  I-BEAMS 

STANDARD   I-BEAMS 

SIZE 

WEIGHT 

WEB 

AREA 

/ 

* 

r 

IN. 

', 

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SIZE 

WEIGHT 

WEB 

AREA 

/ 

s 

r 

4 

r-i 

SIZE 

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WEB 

AREA 

/ 

5 

r 

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Tt 

SIZE 

WEIGHT 

WEB 

AREA 

/ 

M 

r 

1, 

r, 

IN. 

LBS./FT. 

IN. 

SQ.IN. 

IN.« 

IN.3 

IN.1 

IN. 

IN. 

LBS./FT 

IN. 

SQ.IN. 

IN.» 

IN.S 

IN. 

IN.« 

IN. 

IN. 

LBS./FT. 

IN. 

SQ.IN. 

IN.* 

IN.3 

IN. 

IN.4 

IN. 

IN. 

LBS./FT. 

IN. 

SQ.IN. 

IN.« 

IN.' 

IN. 

IN.« 

IN. 

27 

90* 

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26.33 

2958.3 

219.1 

10.60 

75.3 

1.69 

12 

55 
50 
45 
40 

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53 

u 
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ft 

16.18 
14.71 
13  24 
11.84 

321.0 
303.4 
285.7 
269.0 

53.5 
50.6 
47.6 
44.8 

4.45 
4.54 
4.65 
4.77 

17.5 
16.1 

14.9 
13  8 
10.1 
9.5 
12.6 

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PROPERTIES   OF   CHANNELS 


323 


IF  THE  THICKNESS   OF  THE   WEB   IS   MORE   THAN  gj  BELOW  AN  EVEN  SIXTEENTH,  THE   NEXT 

LOWER  SIXTEENTH    18  GIVEN    IN  THE  TABLE   BELOW 

/  =THE  MOMENT  OF  INERTIA  OF  THE  CROSS  SECTION  ABOUT  THE  AXIS  1-1 

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0  46 

1.96 

« 

.18 

A 

1.55 

3.8 

19 

1  56 

03 

03 

0.45 

0.46 

2.08 

25 

62 

i 

7  35 

70.7 

15  7 

3  10 

3.0 

.4 

0.64 

0  62 

4  83 

9 

20 

.45 

A 

5  88 

60.8 

13.5 

3  21 

25 

2 

0.65 

0.58 

5.14 

6 

36 

1 

1  76 

21 

1.4 

1.08 

0.3 

0.3 

0.42 

0.46 

1.10 

15 

.29 

I 

4.41 

50.9 

11.3 

3  40 

2.0 

.0 

0.67 

0.59 

5.49 

3 

5 

.26 

I 

1  47 

1.8 

1.2 

1  12 

03 

0.2 

0.42 

0.44 

1.17 

1SJ 

.23 

A 

3.89 

47.3 

10.5 

3  49 

1.8 

.0 

0.67 

0.61 

5  62 

4 

.17 

i 

1.19 

1.6 

1.1 

1.17 

0.2 

0.2 

041 

0  44 

1.29 

324 


PROPERTIES  OF  BETHLEHEM   I-BEAMS  AND  GIRDER   BEAMS,  AND   LIST  OF  SHIPPING   MARKS 


IF  THE   THICKNESS   OF  THE   WEB    IS    MORE  THAN   $|   BELOW  AN  EVEN  SIX 
TEENTH.  THE    NEXT   LOWER   SIXTEENTH  IS  GIVEN  IN  THE  TABLE  BELOW 

/  =  THE  MOMENT  OF  INERTIA  OF  THE  CROSS  SECTION  ABOUT  THE  AXIS  1-1 
/  1            s  =  THE  CORRESPONDING  SECTION   MODULUS  ABOUT  THE  AXIS  1-1 
r  =  THE  CORRESPONDING  RADIUS  OF  GYRATION  ABOUT  THE  AXIS  1-1 
'      T     '           /s=  THE  MOMENT  OF  INERTIA  OF  THE  CROSS  SECTION  ABOUT  THE  AXIS  2-2 
r2=THE  CORRESPONDING  RADIUS  OF  GYRATION  ABOUT  THE  AXIS  2-2 

EACH  MEMBER  WHICH  IS  SHIPPED  SEPARATELY  SHOULD  BE  MARKED  WITH  A  CHAR- 
ACTERISTIC LETTER  OR  LETTERS  FOLLOWED  BY  A  SPECIFIC  NUMBER.  THUS  :  8  14,  LG2. 
ALL  MEMBERS  WHICH  ARE  INTERCHANGEABLE,  EXCEPT  OFFICE  BUILDING  COLUMNS.* 
SHOULD  BEAR  THE  SAME  MARKS. 
MEMBERS  WHICH  ARE  EXACT  OPPOSITES  SHOULD  BE  MARKED  RIGHT  AND  LEFT 
THUS:  C  )8«.  C  76S  THE  ONE  SHOWN  ON  THE  DRAWING  BEING  THE  RIGHT. 
IN  ALL  OTHER  CASES,  MEMBERS  SHOULD  BEAR  DIFFERENT  MARKS. 
THE  MORE  COMMON  CHARACTERISTIC  LETTERS  USED  FOR  SHIPPING  MARKS  (ADAPTED 
FROM  THE  STANDARDS  OF  THE  AMERICAN  BRIDGE  COMPANY)  ARE  GIVEN  BELOW:  — 

BUILDING   WORK 

BRIDGE  WORK 

ANGLE  BRACING 

D 

ANGLE  B 

BED  PLA 

BRACKET 
BUCKLE 
CAST  PE 
CROSS  F 
END  POS 
FLOOR  B 
GIRDERS 

KNEE   BR 
MISCELL 

PINS  

RACINC 

TES,  E> 
Fl 

S  
)   PLAT 
DESTAL 
RAMES 
TS  

,  BETWEEN  S' 
BOTTOM    LAT 
TOP 
PANSION    END 
XED   END  

rRINGERS....   D 
ERALS    L 

!  BEARING  PLATES  

MP 

BETHLEHEM    I-BEAMS 

BETHLEHEM    GIRDER    BEAMS 

CAST  BASES      . 

CB 

HP 

CASTINGS:  MISCELLANE 

COLUMNS  AND  POSTS,  M 
OFFICE  BUIL 
CRANE  STOPS 
FLOOR  PLATES  

OUS,  STANDARD  A 
SPECIAL  N 
ILL  BUILDINGS,  ETC.   C 
3INGS                                       ' 

FP 

SIZE 

WEIGHT 

WEB 

AREA 

/ 

• 

r 

/2 

r,. 

SIZE 

WEIGHT 

WEB 

AREA 

/ 

S 

r 

A 

r. 

B 

:s 

BP 

S  

CP 

IN. 

LBS./FT. 

IN. 

SQ.IN. 

IN.« 

IN.8 

IN. 

IN.4 

IN. 

IN. 

LBS./FT 

IN. 

SQ.IN. 

IN.* 

IN.3 

IN. 

IN.4 

IN 

..  cs 

FP 

CF 

EP 

30 

120 

.54 

1 

35.30 

5239.6 

349.3 

12.18 

165.0 

2.16 

30 

200 
180 

.75 
.69 

J 
I) 

58.71 
53.00 

9150.6 
S194.5 

610.0 
546.3 

12.48 
12.43 

630.2 
433.3 

3.28 
2.86 

GIRDERS,  PLATE                                                        Gt 

PLATE 
LATTK 
ACES. 
ANEOU 

:ED   '.  ' 

B 

"           LATTICED  L6 
HOPPERS,  BINS,  AND  CHUTES  H 
I-BEAMS  ANDCHANNELS,  MILL  BUILDINGS,  ETC.  B 
OFFICE          "                    ,      { 
KNEE  BRACES  K 

LB 

28 

105 

.50  i 

30.88 

4014.1 

286.7 

11.40 

131.5 

2.06 

K 

5  ANGLES.   . 

..   M 

26 

90 

.46/8 

28.49 

2977.2 

229.0 

10.60 

101.2 

1.95 

PLATES  P 
PANEL  POINT  LETTER 

28 

180 
165 

.69 
.00 

14 
1 

52.86 
48.47 

7264.7 
6562.7 

518.9 
468.8 

11.72 
11.64 

533.3 
371.9 

3.18 
2.77 

24 

84 
83 
73 

.46 
.52 

.39 

A 

J 

I 

24.80 
24.59 
21.47 

2381.9 
2240.9 
2091.0 

198.5 
186.7 
174.3 

9.81 
9.55 
9.87 

91.1 
78.0 
74.4 

i.c: 

1.78 
1.86 

MISCELLANEOUSANGLES,  PLATES,  BRACKETS  M 
PURLINS                                                                           P 

RAILING 
ROLLER 
SHOES,  E 
F 
SHOE  ST 
SPLICE  F 
STRINGS 
STRUTS, 

TRUSSES 
TRUSS   M 

U 

POSTS 

H 
P 

NESTS 

KN 

RAFTERS  

..  H 

XPANSION.. 

.     RS 

26 

160 
150 

.63 

.63 

1 

I 

46.91 
43.94 

5620.8 
5153.9 

432.4 
396.5 

10.95 
10.83 

435.7 
314.6 

3.05 
2.68 

RAILINGS     . 

R 

IXED.. 

FS 

20 

82 
72 
69 
64 
59 

.57 
.43 
.52 
.45 
.38 

f, 
A 
5 
rt 
1 

24.17 
21.37 
20.26 
18.86 
17.36 

1559.8 
1466.5 
1268.9 
1222.1 
1172.2 

156.0 
146.7 
126.9 
122.2 
117.2 

8.03 
8.28 
7.91 
8.05 
8.22 

79.9 
75.9 
51.2 
49.8 
48.3 

1.8: 

1.88 
1.59 
1.62 
1.6C 

RAILING  POSTS 

P 

RUTS 

ES 

RODS,  BRACING       / 
TIE  AND   SAG,  LENGTH   IN    INS.,  THUS:  @ 
SIDE  WALL,  PARTITION,  &  CEILING   FRAMING  F 
SMOKE   FLUES  XF 

LATES 
RS... 
BCTTOI 

TOP 
PORTAL 
SWAY   ! 
,  COMP 
EMBER 

'          U 

SP 

.    S 

II    LATERAL  

..  BS 

24 

140 
120 

.60 
.53 

Vs 
J 

41.16 
35.38 

4201.4 
3607.3 

350.1 
300.6 

10.10 
10.10 

346.9 
249.4 

2.90 
2.66 

TS 

SPLICE  PLATES.. 

SP 

PS 

STRUTS  

s 

iRACIN 
LETE.. 
S  

2           U 

SB 

TRUSSES,  COMPLETE... 

r 

....   T 

18 

59 
54 
52 

48i 

.50 
.41 
.38 

.32 

1 
I 
1 

A 

17.40 
15.87 
15.24 
14.25 

883.3 
842.0 
825.0 
798.3 

98.1 
93.6 
91.7 
88.7 

7.12 
7.28 
7.36 
7.48 

39.1 
37.7 
37.1 
36.2 

1.5C 
1.54 
1.56 
l.Sf 

TRUSS  MEMBERS  

AS  FOLLOWS:  — 

AS  FOLL 
3           U2           L 

OWS:  — 

20 

140 
112 

64 
55 

i 

A 

41.19 
32.81 

2934.7 
2342.1 

293.5 
234.2 

8.44 
8.45 

348.9 
239.3 

2.91 
2.70 

i 

Lf~~~> 

>!' 

^ 
^V, 

/ 

X 

\ 

X 

X 

/ 

15 

71 
64 
54 
46 
41 
38 

.52 
.61 
.41 
.44 

.34 

.29 

1 

™ 
1 
it 
A 
j 

20.95 
18.81 
15.88 
13.52 
12.02 
11.27 

796.2 
664.9 
610.0 
484.8 
456.7 
442.6 

106.2 
88.6 
81.3 
64.6 
60.9 
59.0 

6.16 
5.91 
6.20 
5.99 
6.16 
6.27 

61.3 
41.9 
38.3 
25.2 
24.0 
23.4 

1.71 

18 

92 

•IS 

A 

27.12 

1591.4 

176.8 

7.66 

182.6 

2.59 

1.55 
1.36 
1.41 
1.44 

15 

140 
104 
73 

80 
60 
43 

!2 
A 

A 

41  27 
30.50 
21.49 

1592.7 
1220.1 
883.4 

212.4 

162.7 
117.8 

6.21 
6.32 
6.41 

331.0 
213.0 
123.2 

2.83 
2.64 

2.39 

LO          LI           L2            L3           L2            LI           LO 

THE   UPPER   PANEL   POINTS  OF  A  BRIDGE 
TRUSS   SHOULD    BE    MARKED  U  1,  U  2,  ETC., 
AND  THE  LOWER  PANEL  POINTS  L  0,  L  1,  ETC.. 
SO  THAT  L  1   IS  UNDER   U  1.     THE  END  POST 
(LO-U1)  SHOULD  BE  MARKED  EP.  BUT  EACH 
OTHER  MEMBER  SHOULD  BEAR  THE  MARKS 
OF  THE  PANEL  POINTS  BETWEEN  WHICH  IT 
EXTENDS.  THUS:  —  t  1-2,  U  1-3,  L  1-U1,  L2-U1. 
THE  MEMBERS  OF  THE  LEFT  HALF  OF  THE 
FAR  TRUSS  SHOULD   BE   DRAWN  AND  CON- 
SIDERED RIGHT,  THE  OTHERS  BEING  MARKED 
ff  AND  L  ACCORDINGLY. 

A            H           G              K               3           H          X 
THE     INTERSECTION     POINTS     OF     ROOF 
TRUSSES  SHOULD  BE  LETTERED.  AND  EACH 
SEPARATE  MEMBER  SHOULD  BEAR  THE  LET- 
TERS AT  THE  ENDS.  THUS:  BG  2,  EK  1«. 
WHEN  TRUSSES  ARE  SHIPPED  IN  SECTIONS. 
SUCH   SECTIONS  MAY  BE  MARKED  PT  (PART 
TRUSS),    UNLESS    SHIPPED    IN    HALVES,   AS 
SHOWN   IN    THE   FIGURE   ABOVE,  WHEN   THE 
HALF    AEG    IS    MARKED   AH,    AND  THE    HALF 
XEB  IS  MARKED  XH,  THE  PEAK  PLATE  BEING 
SHIPPED  ON  THE  AH  HALF. 

12 

36 
32 
28f 

,:u 
,34 
.25 

A 
A 

! 

10.61 
9.44 
8.42 

269.2 
228.5 
216.2 

44.9 
38J 
36.0 

5.04 
4.92 
5.07 

21.3 
16.0 
15.3 

1.42 
1.30 
1.35 

12 

70 
55 

46 
37 

A 

1 

20.58 
16.18 

538.8 
432.0 

89.8 
72.0 

5.12 
5.17 

114.7 
81.1 

2.36 
2.24 

10 

28J 
23  J 

.39 
.25 

I 

1 

8.34 
6.94 

134.6 
122.9 

26.9 
24.6 

4.02 
4.21 

12.1 
11.2 

1.21 
1.27 

10 

44 

31 

ft 

12.95 

244.2 

48.8 

4.34 

57.3 

2.10 

9 

24 
20 

?,- 
.25 

: 
: 

7.04 
6.01 

92.1 
85.1 

20.5 
18.9 

3.62 
3.76 

8.8 
8.2 

1.12 
1.17 

9 

38 

30 

f,: 

11.22 

170.9 

38.0 

3.90 

44.1 

1.98 

*   Each  office  bui  Iding  column  should   bear  either  the  Numbers  of  the  Tloors  between  v, 
else  the  Letters  of  the  floors  which   it   supports.     Thus:—  Col.    13   (0-2)   or  AB   73:  Col. 
Office   building  columns  should    be   numbered  consecutively  on  the  plans  so  that  no  two  be 
even  though  alike.     The  same  number  should  be  mainta  ned  from  the  basement  to  the  roof, 
is  spliced  to  the  top  of  section  EF  16.      t   Each  office  building  girder  should  bear  the  floor 
to  the  mark,  thus:  —  67  (2ND  p|.)      J   Each  office  budding  beam  should  bear  either  the  n 
of  theflooi  for  which  it  is  intended,  thus:  —  -40—  I  ST  pi.  or  A  40;   f  I  5  —  8™  Fl.  or  F  IS.   f 

jxtends,  or 
or  EF  25 
ame   mark, 
tion  GH  16 
n  addition 
the  letter 
of  or  R  30; 

ar  the  s 
:hus  sec 
lumber 
jmber  o 
30  —  Re 

8 

195 
17j 

.33 
.25 

A 

: 

5.78 
5.18 

69.6 
'57.4 

15.1 
14.3 

3.24 
3.33 

6.7 
6.4 

1.08 
1.11 

8 

32j 

29 

1 

9.54 

114.4 

28.6 

3.46 

32.9  1.86 

PROPERTIES   OF   STANDARD   ANGLES 


325 


EQUAL  LEGS                                w  jif 

UNEQUAL  LEGS                                         M     Li| 

ADOPTED  1010  BY  ASSOCIATION  OF  AMERICAN        S-{^^  riS 

ADOPTED  1910  BY  ASSOCIATION  OF  AMERICAN  STEEL                    ;.—  (N^-     .'  L        * 

STEEL  MANUFACTURERS                                          L  ,  \'M 

MANUFACTURERS 

o             M 

SIZE 

THICK- 
NESS 

WEIGHT 
PER  FT. 

AREA 

IB 

SS 

rs 

X 

rx 

SIZE 

THICK- 
NESS 

WEIGHT 
PER  FT. 

AREA 

's 

•a 

rs 

X 

'L 

*L 

TL 

y 

ra 

INCHES 

INCHES 

POUNDS 

SQ.  IN. 

IN.« 

IN." 

IN. 

IN. 

IN. 

INCHES 

INCHES 

POUNDS 

SQ.  IN. 

IN.4 

IN.* 

IN. 

IN. 

IN.« 

IN.* 

IN. 

IN. 

IN. 

li 

98.0 

17.5 

2  42 

2.41 

1.55 

J 

27.7 

7.2 

.86 

2.12 

9.8 

3.4 

1.11 

.12 

0.86 

1A 

54.0 

15.87 

93.5 

16.7 

2.43 

2.39 

1  56 

11 

25.4 

7.47 

26.1 

6.7 

.87 

2.10 

9.2 

3.2 

1.11 

.10 

0.86 

1 

51.0 

15.00 

89.0 

15.8 

2  44 

2.37 

1  56 

23.6 

6.94 

24.5 

8.2 

.88 

2.08 

8.7 

3.0 

1.12 

.08 

0.86 

8x8 

1! 
H 

48.1 
45.0 
42.0 

14.12 
13  23 
12.34 

84  3 
79.6 
74.7 

14.9 
14.0 

13.1 

2.44 
2.45 
2.46 

2.34 
2.32 
2.30 

1  56 
1  56 

1.57 

6x4 

U    i 
*1 

21.8 
20.0 
18.1 

16.2 

6.40 
5.86 
5.31 
4.75 

22.8 
21.1 
19.3 
17.4 

5.8 
5.3 
4.8 
4.3 

.89 
.90 
.90 
.91 

2.06 
2.03 
2.01 
1.99 

8.1 
7.5 
6.9 
6.3 

2.8 
2.5 
2.3 
2.1 

1.13 
1.13 
1.14 
1.15 

.08 
03 
.01 
0.99 

0.86 
0.86 
0.87 
0.87 

! 

38.9 

11.44 

69.7 

12.2 

2.47 

2.28 

1.57 

A 

H.3 

4.18 

15.5 

3.8 

.92 

1.96 

5.6 

1.8 

1.16 

0.96 

0.87 

H 

35.8 

10.53 

64.6 

11.2 

2.48 

2.25 

1.58 

i 

12.3 

3.61 

13.5 

3.3 

.93 

1.94 

4.9 

1.6 

1.17 

0.94 

0.88 

i 

32.7 

9.61 

59.4 

10.3 

2.49 

2.23 

1.58 

X 

25.7 

7.55 

26.4 

7.0 

.87 

2.22 

66 

2.6 

0.93 

0.97 

0.75 

18 

29.6 

8.68 

54.1 

9.3 

2.50 

2.21 

1.58 

M 

24.0 

7.06 

24.9 

6.6 

.88  • 

2.20 

6.2 

2.4 

0.94 

0.95 

0.75 

J 

26.4 

7.75 

48.6 

8.4 

2.51 

2.19 

1.58 

1 

22.4 

6.56 

23.3 

6.1 

.89 

2.18 

5.8 

2.3 

0  94 

0.93 

0.75 

1 

37.4 

11.00 

35.5 

86 

1.80 

1.86 

1.16 

6x3? 

51  ; 

20.6 
18.9 

6.06 
5.55 

21.7 
20.1 

5.6 
5.2 

.89 
.90 

2.15 
2.13 

5.5 
5.1 

2.1 

.9 

0.95 
0  96 

0.90 
0  88 

0.75 
0.75 

H 

35.3 

10.37 

33.7 

8.1 

1.80 

1.84 

1.16 

V         V/U 

A 

17.1 

5.03 

18.4 

4.7    • 

.91 

2.11 

4.7 

.8 

0.96 

0  86 

0.75 

i 

33.1 

9.73 

31.9 

7.6 

1.81 

1.82 

1.17 

i 

15.3 

4.50 

16.6 

4.2 

.92 

2.08 

4.3 

.6 

0.97 

0.83 

0.76 

it 

31.0 

9  09 

30.1 

7.2 

1.82 

1.80 

1.17 

£ 

13.5 

3.97 

14.8 

3.7 

.93 

2.08 

3.8 

.4 

0.98 

0.81 

0.76 

i 

28.7 

8.44 

28.2 

6.7 

1.83 

1.78 

1.17 

j 

11.7 

3.42 

12.9 

3.3 

.94 

2.04 

3.3 

.2 

0.99 

0.78 

0.77 

6x6 

U 

26.5 

7.78 

26.2 

6.2 

.83 

1.75 

1.17 

5 

19.8 

5.81 

13.9 

4.3 

.55 

1.75 

5.6 

.2 

0.98 

1.00 

0.75 

Vr        W 

i 

24  2 

7.11 

24.2 

5.7 

84 

1.73 

.17 

U 

18.3 

5.37 

13.0 

4.0 

.56 

1.72 

5.2 

.1 

0.98 

0.97 

0  75 

A 
J 

21.9 
19.6 

6.43 
5.75 

22.1 
19.9 

51    i 

4.6 

.85 
.86 

1.71 
1.68 

.18 
.18 

5x31 

*i 

16.8 
15.2 
13.6 

4.92 
4.47 
4.00 

12.0 
11.0 
10.0 

3.7 
3.3 
3.0 

.56 
.57 
.58 

1.70 
68 
66 

4.8 
4.4 
4.0 

.9 

.7 
.6 

0.99 
1.00 
1  01 

0.95 
0.93 
0.91 

•  0.75 
0  75 
0.75 

A 

17.2 

5  06 

17.7 

4.1 

.87 

1.66 

.19 

A 

12.0 

3.53 

8.9 

2.6 

.59 

.63 

3.6 

.4 

1.01 

0.88 

0.78 

1 

14.9 

4  36 

15.4 

3.5 

.88 

1  64 

.19 

i 

10.4 

3.05 

7.8 

2.3 

.60 

.61 

3.2 

.2 

1  02 

0.86 

0  76 

1 

18.5 

S.44 

7.7 

2.8 

.19 

1.27 

0.77 

ft 

8.7 

2.56 

6.6 

1.9 

.61 

.59 

2.7 

.0 

103 

0.84 

0.76 

H 

17.1 

5.03 

7.2 

2.6 

.19 

1.25 

0.77 

H 

17.1 

5.03 

12.3 

3.9 

1.56 

.82 

3.3 

.5 

0.81 

0  82 

0.64 

| 

15.7 

4.61 

6.7 

2.4 

.20 

1.23 

0.77 

1 

15.7 

4.61 

11.4 

3.5 

1.57 

.80 

3.1 

.4 

0  81 

0.80 

0.64 

4x4 

A 

1 

14  3 
12.8 

4.18 
3.75 

8.1 
5.6 

2.2 
2.0 

.21 
.22 

1.21 
1.18 

0^78 
0.78 

5x3 

A 

IS 

14.3 

12.8 
11.3 

4.18 
3.75 
3.31 

10.4 
9.5 
8.4 

32 
2.9 

2.6 

1.58 
1.59 
1.60 

.77 
.75 
.73 

2.8 
2.6 
2.3 

.3 
.1 
.0 

0.82 
0.83 
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0.77 
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326 


PROPERTIES   OF   SPECIAL   ANGLES 


EQUAL  AND    UNEQUAL   LEGS                            g| 

•  NOT   ROLLED    BY   ALL  THE    LEADING    STEEL   COMPANIES                |JL. 
FOR  ADDITIONAL  SECTIONS   SEE    PAGE  303                             $ 

UNEQUAL   LEGS                                        ^ 

•  NOT    ROLLED  BY  ALL  THE   LEADING  STEEL  COMPANIES             i.—  ft 
FOR  ADDITIONAL   SECTIONS    SEE    PAGE  303 

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0.74 
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TWO  ANGLES  IN  TENSION 


327 


NET  AREAS  IN  SQ.  INS.,  AND  ALLOWABLE  TENSILE  STRENGTH  IN  THOUSANDS  OF  LBS.  AT  16,000  LBS.  PER  SQ.  IN.,  FOR  TWO  ANGLES 

EQUAL  LEGS 

UNEQUAL  LEGS 

DIAM.  OF  HOLES 
'/a'  LARGER  THAI* 
OIAM.  OF  RIVETS 

ONE  HOLE  IN   EACH  ANGLE 
DEDUCTED 

TWO  HOLES   IN   EACH  ANGLE 
DEDUCTED 

DIAM.  OF  HOLES 
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DIAM.  OF  RIVETS 

ONE  HOLE  IN  EACH  ANGLE 
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TWO  HOLES  IN   EACH  ANGLE 
DEDUCTED 

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UNIT  STRESSES  FOR  COMPRESSION 


/  =  LENGTH  OF  MEMBER  IN   INCHES                                 UNIT    STRESSES    IN    THOUSANDS    OF             FOR  VALUES  BELOW      HE 
r=LEA8T  RADIUS  OF  GYRATION  IN  INCHES                  LBS.    PER     SO.  IN.  AT  I6.0OO-70  1.  r  FOR                  "           "           BETWEEN 
VALUES  BELOW  DASHED  LINES  EXCEED  14,000                 DIFFERENT^  VALUES    OF  /   AND    r                        "           "          ABOVE 

AVYFULL  LINES  THE  RATIO  IT  DOES  NOT  EXCE 

ED  100 
120 
160 

LENGTH    OF    MEMBER    IN    FEET 

r 

3 

10 

11 

12 

13 

14 

15 

16  |  17 

18 

19 

20 

21 

22  |  23    24    25 

26 

27 

28 

29 

30 

31     32 

33 

34 

35 

36 

37 

38     39 

40 

41 

42 

43 

44     46 

46 

47 

48 

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0.9 
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1.1 
1.2 
1.3 
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1.6 
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9.6 
9.7 

9.8 

10.0 
10.1 
1U.L 
10.3 

a.l 
9.3 
9.5 
9.C 

9.8 
10.0 
,0.1 
10.3 
10.4 
10.5 
10.7 
10.8 
10.9 
11.0 

11.1 

11.2 
11.3 

11.4 
11.5 
11.6 

11.6 
11.7 
11.8 
11.  C 
11.  C 
12.0 
12.1 

5.6 
5.9 
6.2 
6.5 
6.7 
6.9 
7.2 
7.4 

5.7 
6.0 
6.2 
6.5 

6.7 
7.0 
7.2 
7.4 
7.0 
7.8 
8.0 
8.1 
8.3 
8.5 
8.6 
8.8 
8.9 
9.1 
9.2 
9.3 
9.4 

9.5 
9.7 
9.8 
9.9 

10.  ( 

9.0 
9.2 

5.7 

6.0 
6.3 

6.5 

6.8 
7.0 

7.2 
7.4 

Tel 

7.8 
8.0 

8.1 
8.3 

8.4 
8.C 

8.7 
8.9 

Tl 

9.2 
9.3 
9.4 

9.5 

9.6 
9.7 

9.8 

5.5 
5.8 

6.0 
6.3 
6.6 
6.8 
7.0 
7.2 
74 

5.6 
5.8 

6.1 
6.3 
6.6 
6.8 
7.0 
7.2 

£ 

?1 

8.1 
8.3 
8.4 
8.6 
8.7 
8.8 
9.0 

9.1 
9.2 
9.3 
9.4 
9.6 

5.6 
5.t 
6.1 
6.4 

6.6 
6.8 
7.0 

2 

TS 

7.9 
8.1 
8.3 
8.4 
8.6 
8.7 
8.8 
9.0 
TT 
9.2 
9.3 
9.4 

5^7 
5.9 
6.2 

6.4 
6.6 
6.8 
7.0 
7.2 
7.4 
T6 
7.8 
7.9 

8.1 

8.2 
8.4 
8.5 
8.7 
8.8 

TO! 
9.2 
9.3 

7.8 
8.0 

8.2 
8.4 

8.6 
8.8 
9.0 

/.i; 
7.8 
8.0 
8.2 
8.4 
8.6 
8.8 
8.9 

"a~T 
9.2 
9.4 
9.5 
9.7 
9.8 
9.9 
,0.0 
10.1 
10.2 
10.3 
10.4 
10.5 
10.6 
10.7 
10..' 

9.4 
9.5 
9.7 
9.8 
10.0 
10.1 
10.3 
10.4 
10.5 
10.6 
10.7 
10.9 
11.0 
11.1 
11.1 
11.2 
11.3 
11.4 

11.5 
11.6 
11.7 
11.7 
11.8 

a.l 

9.3 
9.5 

9.0 
9.8 
9.9 
10.1 
10.2 
10.3 
10.5 
10.6 
10.7 
,0.8 

10.9 

11.0 

11.1 

11.2 
11.3 

n.;: 

11.4 
11.5 
11.6 
11.7 

7.6 
7.8 
8.0 
8.2 

8.3 
8.5 
8.6 
8.8 
8.9 
9.1 
9.2 
9.3 
9.5 
9.6 
9.7 
9.8 
9.9 
10.0 
,10.1 

9.1 
9.3 
9.4 
9.6 
9.7 
9.8 
9.9 
10.1 
10.2 
10.3 
10.4 
10.5 
10.6 
10.7 
10.8 
10.9 
,1.0 

7.0 

7.8 
7.9 
8.1 
8.3 
8.4 
8.6 
8.7 
8.1 

9.0 
9.1 
9.2 

9.4 
9.5 
9.C 
9.7 

TWO  ANGLE  STRUTS -RADII  OF  GYRATION 


329 


RADII  OF  GYRATION  IN  INCHES  FOR  TWO  ANGLES  ARRANGED  AS  SHOWN 

a 

a 

EQUAL  LEGS 

^P 

UNEQUAL  LEGS 

"a       [IpT3 

i 

B 

THICK- 

AREA 

AXIS 

DISTANCES  TO  B.  OF  ANGLES—  AXIS  BB 

THICK- 

AREA 

AXIS 

DISTANCE  B.  TO  B.  OF  ANGLES  —  AXIS  BB 

AXIS 

DISTANCE  B.  TO  B.  OF  ANGLES  —  AXIS  BB 

SIZE 

NESS 

2  Ls 

AA 

0 

A 

1 

A 

* 

A 

1 

NESS 

2  Ls 

AA 

0 

A 

1 

8 

A 

i 

A 

f 

AA 

0 

A 

t 

A 

i 

A 

1 

Ii 

33  46 

2.42 

3  42 

3.53 

3.55 

3  57 

3.60 

3  62 

3.64 

i 

15.96 

1.86 

1.58 

1.69 

1.71 

1.74 

1.76 

1.79 

1.81 

1.11 

2,82 

2  94 

2.97 

2.99 

3.01 

3.04 

3.06 

1A 
l 

H 

31.74 
30  00 
28.24 

2.43 
2.44 
2.44 

3  41 

3  40 
3.38 

3.52 
3.51 
3.49 

3.54 
3  53 
3.52 

3  56 
3.55 
3.54 

3.59 
3.58 
3.56 

3  61 
3.60 
3.58 

3.63 
3.62 
3.61 

6x4 

! 

14.94 
13.88 
12.80 
11.72 

1.87 
1.88 
1.89 
1.90 

1.56 
1.66 
1.55 
1.53 

1.68 
1.67 
1.6C 
1.64 

1.70 
1.69 
1.68 
1.66 

1.73 
1.72 
1.71 
1.69 

1.75 
.74 
.73 
.71 

1.77 
1.76 
1.75 
1.73 

1.80 
1.79 
177 
1  76 

1.11 
1.12 
1.13 
1.13 

2  81 
2.80 
2.79 
2  78 

2  93 
2.92 
2.91 
2.89 

2.96 
2.95 
2.94 
2.92 

2.98 
2.97 
2.96 
2.94 

3  00 
2  99 
2.98 
2.97 

3.03 
3  02 
3.01 
2.99 

3  05 
3.04 
3.03 
3  01 

i 

26.46 

2.45 

3.38 

3  48 

3.51 

3  53 

3.55 

3.57 

3.60 

\J             1 

A 

10  62 

1.90 

.52 

1  63 

1.65 

1.68 

.70 

.72 

1.75 

1.14 

2.77 

2.88 

2.91 

2.93 

2.95 

2.98 

3.00 

8x8 

ii 

24.68 

2.46 

3  37 

3  48 

3.50 

3  52 

3  54 

3.57 

3.59 

i 

9.50 

1.91 

1.52 

1.62 

1.65 

1.67 

.69 

.71 

1.74 

1.15 

2.76 

2.88 

2.90 

2.92 

2.95 

2.97 

2.99 

V          V 

22.88 

2.47 

3.36 

3.47 

3.49 

3  51 

3.54 

3  56 

3.58 

A 

8.36 

1.92 

1.50 

1.61 

1.63 

1.65 

.68 

.70 

1.72 

1.16 

2.75 

2.86 

2.88 

2.91 

2.93 

2.95 

2.98 

ii 

21.06 

2.48 

3.35 

3.46 

3.48 

3.50 

3.52 

3.54 

3.57 

i 

7.22 

1.93 

1.50 

1.60 

1.62 

1  64 

.67 

.69 

1.71 

1.17 

2.74 

2.85 

2.87 

2.90 

2.92 

2.94 

2.97 

i 

19  22 

2.49 

3  34 

3.46 

3.47 

3.49 

3  51 

3.54 

3.56 

i 

15.10 

1.87 

1.34 

1.46 

1.49 

1.51 

.53 

.56 

1.58 

0.93 

2.90 

3.02 

3  05 

3.07 

3.10 

3.12 

3.15 

A 

17.36 

2.50 

3.33 

3.44 

3.46 

3.48 

3.50 

3  53 

3.55 

H 

14.12 

1.88 

1.34 

1  45 

1.48 

1  50 

.52 

.55 

1.57 

0.94 

2.89 

3.01 

3.04 

3.06 

3.09 

3.11 

3.14 

15.50 

2.51 

3.33 

3.44 

3.45 

3.48 

3.50 

3-'.  52 

3.54 

i 

13.12 

1.89 

1.32 

1.44 

1.46 

1.48 

.51 

.53 

1.56 

0.94 

2.88 

3.00 

3.03 

3.05 

3.08 

3.10 

3  13 

ii 

12.12 

1.89 

1  31 

1.42 

1.45 

1.47 

.49 

.52 

1.54 

0  95, 

2.86 

2.98 

3.01 

3.03 

3.06 

3.08 

3.11 

i 

22.00 

1.80 

2  59 

2.70 

2.72 

2.75 

2.77 

2.80 

2.82 

C  v^  O  1 

n  X  ,  io 

1 

11.10 

1.90 

1.30 

1.41 

1.43 

1.46 

.48 

.51 

1.53 

0.96 

2.85 

2.97 

3.00 

3.02 

3  05 

3.07 

3.10 

18 

20.74 

.80 

2.58 

2.69 

2.71 

2.74 

2.76 

2.78 

2.81 

v  "  V/2 

A 

10.06 

1.91 

1.29 

1.40 

1.42 

1  44 

.47 

.49 

1.52 

0.96 

2.85 

2.96 

2.99 

3.01 

3.04 

3.06 

3.09 

j 

19.46 

.81 

2.57 

2.68 

2.70 

2.73 

2.75 

2.77 

2.80 

i 

9.00 

1.92 

1.28 

1.38 

1.41 

1.43 

.45 

.48 

1.50 

0.97 

2.83 

2.95 

2.97 

3.00 

3.02 

3.04 

3.07 

U 

18.18 

.82 

2.56 

2.67 

2.69 

2.72 

2.74 

2.76 

2.79 

A 

7.94 

1.93 

1.27 

1.37 

1.40 

1.42 

.44 

.47 

.49 

0.98 

2.82 

2.94 

2.96 

2.99 

3.01 

3.03 

3.06 

16  88 

.83 

2.55 

2.66 

2.68 

2.71 

2.73 

2.76 

2.78 

i 

6.84 

1.94 

1.26 

1.36 

1.39 

1.41 

.43 

.45 

.47 

0  99 

2  81 

2  93 

2.95 

2.98 

3.00 

3.02 

3.05 

6x6 

« 

15.56 

.83 

2  53 

2.64 

2.67 

2.69 

2.71 

2.74 

2.76 

j 

11.62 

1.55 

1.40 

1.51 

1.54 

1.56 

.59 

.61 

.63 

0.98 

2.34 

2.46 

2.48 

2.51 

2.53 

2.55 

2.58 

\J  r*   \J 

14.22 

1.84 

2.53 

2.64 

2.66 

2.68 

2.71 

2.73 

2  75 

ii 

10.74 

1.56 

1.38 

1.49 

1.52 

1  54 

.57 

.59 

.61 

0  98 

2.32 

2  44 

2.46 

2.49 

2.51 

2.53 

2  56 

A 
A 

12.86 
11.50 
10.12 

1.85 
1.86 
1.87 

2.52 
2.51 
2.50 

2.63 
2.62 
2.61 

2.65 
2.64 
2.63 

2.67 
2.66 
2.65 

2.70 
2.68 
2  67 

2.72 
2.70 
2.69 

2.74 
2.73 
2.72 

5x32L 

A 

9.84 
8.94 
8.00 
7.06 

1.56 
1.57 
1.58 
1.59 

1.37 
1.37 
1.36 
1.34 

1.49 
1.48 
1.47 
1.45 

1.51 
1.50 
1.49 
1.47 

1.53 
1.62 
1.51 
1.50 

.56 
.55 
.54 

.52 

.58 
.57 
.56 
.54 

.60 
.59 
.58 

57 

0  99 
1.00 
1.01 

1.01 

2.31 
2  30 
2.29 
2  28 

2.43 
2.42 
2.41 
2.39 

2  45 
2  44 
2  43 

2.42 

2.48 
2  46 
2.45 
2.44 

2.50 
2.49 
2.48 
2.46 

2  52 
2  51 
2.50 
2.49 

2.55 
254 
2.53 
2.51 

i 

8.72 

1.88 

2.49 

2.60 

2.62 

2.64 

2.66 

2.69 

2.71 

i 

6.10 

1.60 

1  34 

1.44 

1  46 

1.49 

.51 

.53 

.55 

1.02 

2.27 

2  38 

2  41 

2.43 

2.45 

2.48 

2.50 

i 

10.88 

.19 

.74 

1.86 

1.88 

1.91 

1.93 

1.95 

1.98 

A 

5.12 

1.61 

1.33 

1.43 

1.45 

1.48 

.50 

.52 

.55 

1.03 

2.26 

2.37 

2.40 

2.42 

2.44 

2.47 

2.49 

ii 

10.06 

.19 

.73 

1.84 

1.87 

1.89 

1.92 

1.94 

1.96 

U 

10.06 

1.56 

1.15 

1.27 

1.29 

1.32 

34 

.37 

.39 

0.81 

2.40 

2.52 

2.54 

2.57 

2.59 

2.62 

2.64 

1 

9.22 

20 

.72 

1  .83 

1.86 

1.88 

1.91 

1  .93 

1.95 

I 

9.22 

1.57 

1.14 

1.25 

1.28 

1  30 

.33 

35 

.38 

0.81 

2.39 

2  51 

2.53 

2  56 

2.58 

2.61 

2.63 

4x4 

A 

8.36 
7.50 

21 
.22 

.71 
.70 

1.83 
1.81 

1.85 
1.83 

1.87 
1.86 

1.90 
1.88 

1.92 
1  90 

1.94 
1.93 

5x3 

A 

8.36 
7.50 
6.62 

1.58 
1.59 
1  60 

1  12 
1.12 
1  11 

1.24 
1  23 
1.22 

1  26 
1.25 
1.24 

1.29 
1.28 
1.27 

.31 
.30 
.29 

.33 
.32 
.31 

36 
.    .35 
.34 

0.82 
0.83 
0.84 

2  37 
2  36 
2.36 

2  49 
2.48 
2.47 

2  52 
2  50 
2.49 

2.54 
2.53 
2.52 

2.57 
2.55 
2.54 

2.59 
2.58 
2.57 

2.61 
2.60 
2  59 

A 

6.62 

1.23 

1.69 

1  80 

1.82 

1.85 

1.87 

1.89 

1.92 

5.72 

1  61 

1.10 

1.21 

1.23 

1.25 

.27 

29 

.32 

0.84 

2.34 

2.46 

2.48 

2.51 

2.53 

2  65 

2.58 

I 

5.72 

1.23 

1.68 

.79 

1.81 

1.84 

1.86 

1.88 

1  90 

A 

4.80 

1.61 

1.09 

1.19 

1.22 

1.24 

.26 

.28 

.31 

0.85 

2.33 

2.44 

2.47 

2.49 

2.52 

2.54 

2  56 

A 

4.80 

1.24 

1.67 

.78 

1.80 

1.83 

1.85 

1.87 

1.89 

I 

7.96 

1.23 

1.22 

1.33 

1  36 

1.38 

.41 

43 

.46 

0.85 

.84 

96 

1.98 

2.01 

2.03 

2.06 

2.08 

§ 

7.96 

1.04 

1.52 

.63 

1.66 

1.68 

1.70 

1.73 

75 

7.24 

1  24 

.21 

1  32 

1.35 

1.37 

.40 

.42 

.45 

0.86 

.83 

.95 

1.97 

2.00 

2.02 

2.05 

2.07 

31%*O1 

A 

7.24 
6.50 

1.05 
1.06 

1  51 
1.50 

.62 
.61 

1.65 
1.64 

1.67 
1.66 

1.69 
1.68 

1.72 
1.71 

.74 

.73 

4x3 

A     t 

6.50 
5.74 
4.96 

1.25 
1.25 
1.26 

.20 
.18 
18 

1.31 
1.29 
1.28 

1.33 
1.32 
1.31 

1.36 
1.34 
1.33 

.38 
.36 
.35 

40 

.39 
38 

.43 
.41 
.40 

0  86 
0.87 
0  88 

.82 
.81 
80 

.94 
.92 
91 

1.96 
.95 
.94 

1.99 
.97 
.96 

2.01 
1.99 
1.98 

2  04 
2.02 
2.01 

2.06 
2.04 
2  03 

2       w2 

A 

5.74 

1.07 

.49 

.60 

1.63 

1.65 

1.67 

70 

.72 

A 

4.18 

1.27 

.17 

1.28 

1.30 

1.32 

.35 

.37 

.39 

0.89 

.79 

.90 

.93 

.95 

1.97 

2.00 

2.02 

i 

4.96 

1.07 

.48 

.59 

1.61 

1.63 

1.66 

.68 

.70 

A 

6.68 

1.07 

1.25 

1.37 

1  39 

1.42 

.44 

47 

49 

0  87 

.57 

.69 

.71 

.74 

.76 

.79 

.81 

A 

4.18 

1.08 

.47 

.58 

1.60 

1.62 

1.65 

.67 

.69 

i 

6.00 

1.07 

1.24 

1.36 

1.38 

1.41 

43 

.46 

.48 

0.88 

56 

.67 

.70 

.72 

.75 

.77 

.80 

i 

5.50 

0.90 

.29 

.41 

.43 

1.46 

.48 

.51 

.53 

*^~X  ^ 

5.30 

1.08 

1.23 

1.34 

1.37 

1.39 

41 

.44 

.46 

0.89 

.54 

.66 

.68 

.71 

.73 

.75 

.78 

3x3 

A 

4.86 
4.22 

0.91 

0.91 

.28 
.27 

40 
.39 

.42 
.41 

1.45 
1.44 

.47 
.46 

.50 
.48 

.52 
.51 

2 

A     ! 

4.60 
3.86 

1  09 
1.10 

1.22 
1  21 

1.33 
1.32 

1.36 
1.35 

1.38 
1.37 

.40 
.39 

43 
.41 

.45 
.43 

0.90 
0.90 

.53 
52 

.65 
.64 

.67 
.66 

.70 
.69 

.72 

.71 

.74 
.73 

.77 
.78 

V  **  VJ 

A 

3.56 

0.92 

.27 

.38 

.40 

1.43 

.45 

.47 

.50 

j 

5.50 

1  09 

0  99 

1.11 

1.13 

1.16 

.18 

.20 

.23 

0  70 

62 

.74 

.76 

.79 

.81 

.84 

.86 

5 

2.88 

0  93 

.25 

36 

.39 

111 

.43 

46 

.48 

OixOi 

I     ' 

4.86 
4.22 

1.09 
1  10 

0.98 
0.97 

1.10 

1.09 

1.12 
1.11 

1.15 
1.14 

.17 
.16 

.19 

.18 

.22 
21 

0.71 
0.72 

.61 
.60 

.73 

.72 

.75 
.74 

.77 
.76 

.80 
.79 

.82 
.81 

.85 
.84 

A 

4.00 

0.75 

1.08 

.20 

.22 

1.25 

1.27 

.30 

.32 

vJ2      ^2 

3.56 

1.11 

0.97 

1.08 

1.10 

1.13 

15 

.17 

.20 

0.73 

.59 

.71 

.73 

.75 

.78 

.80 

.83 

1 

3.46 

0.75 

1.07 

.18 

.21 

1.23 

1.26 

.28 

.31 

i 

2.88 

1.12 

0.96 

1.06 

1.09 

1.11 

.13 

.16 

.18 

0.74 

.58 

.69 

.71 

.74 

.76 

.79 

.81 

21x23 

A 

2.94 

0.76 

1.06 

.18 

.20 

1.22 

1.25 

.27 

.30 

A 

4  42 

0.92 

1.03 

1.15 

1.17 

1  20 

.22 

.25 

.27 

0.73 

.34 

.46 

.49 

.51 

.54 

.56 

.59 

j 

2.38 

0.77 

1.05 

1.17 

.19 

1  21 

.24 

.26 

.29 

O       O  ' 

i 

3.84 

0  93 

1.02 

1.14 

1.16 

1.19 

.21 

.24 

.26 

0.74 

.34 

.45 

.48 

.50 

.53 

.55 

.58 

1.80 

0.78 

1.04 

1  .15 

.18 

1.20 

22 

.25 

.27 

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A 

3.24 

0.94 

1.01 

1.12 

1.14 

1.17 

.19 

.21 

.24 

0.74 

.32 

.43 

.46 

.48 

.51 

.53 

.56 

i 

2.62 

0.95 

1.00 

1.11 

1.13 

1.16 

1.18 

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0.75 

.31 

.42 

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.50 

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i 
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2.72 
2  30 
1.88 

0.59 
0  60 
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0.86 
0.85 

0.99 
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0.96 

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1.04 
1.02 
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3  10 
2.62 
2.12 

0.77 
0.78 
0.78 

0.82 
0.81 

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0  94 
0.93 
0.91 

0.96 
0.95 
0.94 

0.98 
0.97 
0.96 

1.01 
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1.04 

1.02 
1.01 

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0.58 
0.58 
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1.28 

33 

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A 

1.42 

0.62 

0.84 

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f. 

1  62 

0.79 

0.79 

0.90 

0  92 

0.94 

0.97 

0.99 

.02 

0.60 

.10 

.21 

1.24 

1.26 

1.29       131 

.33 

330 


SINGLE  ANGLE  STRUTS-SAFE   LOADS 


;  =  LENGTH  OF  MEMBER  IN   INCHES                           SAFE    LOADS     IN    THOUSANDS    OF          FOR  VALUES  TO  THE  LEFT  O 
r=  LEAST  RADIUS  OF  GYRATION  IN  INCHES                      POUNDS  AT  IR  nnn      TO  7/r                                                      BETWEEN 
•  UNIT  STRESS  EXCEEDS  14.000  POUNDS                          PUUINU&  AT  I6.OOO  -                                       THE  R|GHT  0 

F  THE  HEAVY  LINES  THE  RATIO  //r  DOES  NOTEXCEE 

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120 
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LENGTH  OF  MEMBER  IN  FEET 

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LENGTH  OF  MEMBER  IN  FEET 

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10 

11 

12 

13 

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17 

18 

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240* 
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125* 
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152 
144 
195 
126 

117 
108 
98 
89 
80 
70 
60 

69 
64 
59 
53 
48 
42 
37 
31 

49 
44 
40 
35 
31 
26 

32 
28 
25 
21 

17 

21 
19 
16 
13 

232 
220 
208 
196 
183 
171 
159 
146 
133 
120 
107 

144 
136 
128 
119 
111 
102 
93 
85 
76 
67 
57 

63 

59 
54 
49 
44 
39 
34 
28 

44 
40 
36 
32 
28 
23 

28 
25 
22 
18 
15 

18 
16 
13 
11 

222 
211 
200 
188 
176 
165 
153 
141 
128 
116 
103 

136 
128 
121 
113 
105 
97 
88 
80 
71 
63 
54 

57 
53 
49 
44 
40 
35 
31 
26 

39 
36 
32 
28 
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213 
202 
191 
180 
169 
158 
146 
135 
123 
111 
99 

128 
121 
114 
106 
99 
91 
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75 
67 
59 
51 

51 

48 
44 
40 
36 
32 
27 
23 

204 
194 
184 
173 
162 
151 
140 
129 
118 
107 
95 

120 
113 
107 
100 
93 
85 
78 
71 
63 
56 
48 

Ui 

185 
175 
165 
155 
145 
134 
124 
113 
102 
91 

112 
106 
100 
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87 
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73 
66 
59 
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177 
167 
157 
148 
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104 
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177 
168 
159 
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122 
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168 
160 
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142 
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159 
151 
143 
135 
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92 
84 
75 

150 

141 

132 
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77 
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104 
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72 
65 
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113 
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103 
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67 
61 
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104 
100 
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89 
83 
78 
73 
68 
62 
56 
50 

95 
92 
87 
82 
76 
72 
67 
62 
57 
51 
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45 
39 
32 

61 
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45 
40 
35 
29 

48 
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39 
35 
30 
25 

40 
36 
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27 
23 

31 
28 
24 
20 
16 

25 
21 
18 

96 
90 
84 
77 
71 
64 
58 
51 
44 

87 
81 
76 
70 
64 
58 
52 
46 
40 

67 
62 
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52 
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41 
35 
30 

54 
50 
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41 
36 
31 
26 

43 
39 
35 
31 
27 
23 

35 
32 
28 
24 
21 

27 

89 
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77 
71 
65 
59 
53 
47 
41 

79 
73 
68 
63 
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52 
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37 
32 

54 
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41 
37 
33 
29 
24 

73 
68 
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54 
49 
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39 
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65 
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52 
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35 
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39 
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26 
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143 
135 
127 
119 
112 
103 
96 
87 
79 
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134 
127 
119 
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105 
97 
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74 
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62 
58 
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49 
45 
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53 
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41 
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25 
22 
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28 
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19 
16 
14 

22 
20 
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16 
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96 
91 
86 
80 
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69 
63 
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88 
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42 
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80 
76 
72 
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33 

72 
68 
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61 
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52 
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39 
34 
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54 
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39 
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28 
24 
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37 
34 
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24 
22 
20 
18 
16 
13 

31 
28 
26 
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18 
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37 
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32 
29 
26 
23 
20 
17 

26 
24 
21 
18 
15 

18 

34 
31 
29 
26 
23 
20 
17 

27 
25 
22 
20 
17 
15 

22 
20 
17 
15 

13 

34 
31 
28 
25 
22 
18 

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18 
15 
13 

29 
27 
24 
21 
19 
16 

16 
14 
12 
11 

24 
21 
18 
16 

13 

14 
13 
11 
9 

11 

11 

10 
8 
7 
5 

9 

21 
17 
14 

21 

18 
16 

17 
15 
12 

18 
15 
13 

14 
12 
10 

14 
12 
11 

8 

13 
11 
9 
7 

10 
8 

7 

15 

15 
13 
11 
8 

13 

12 

10 
8 

7 

11 

9 
8 
6 
5 

5 

4 

SIZE 

THICK- 
NESS 

3 

4 

5 

6 

7 

8 

9 

10 

11 

13 

13 

14 

15 

16 

17 

18 

19 

SIZE 

THICK- 
NESS 

3 

4 

5 

6 

7 

8 

9 

10 

11 

LENGTH  OF  MEMBER  IN  FEET 

LENGTH  OF   MEMBER   IN   FEET 

TWO  ANGLE  STRUTS-SAFE   LOADS 


331 


SAFE  LOADS  IN  THOUSANDS  OF  POUNDS  AT  16,000  —  70  //r.   FOR  EXPLANATIONS  SEE  PRECEDING  PAGE 

LEAST  RADIUS  ABOUT  AXIS  BB  FOR  5X3  Ls  OR  OVER.  AND  3Vi  X  2'/2  X  Vi  AND  3'/2  X  2'/2  X  Vie 
LEAST  RADIUS  ABOUT  AXIS  AA  FOR  4X3  Ls  OR  UNDER  EXCEPT  8ViX2ViXy5  AND  3'/2X2'/2  X  Vie 
ANY  DISTANCE  APART  FOR  3VaX3.  3  X  2</2  AND  2!/2  X  2 
=»/•'  B.  TO  B.  FOR  ALL  OTHER  ANGLES                                                                                                                                            IJ» 

LEAST  RADIUS  ABOUT  AXIS  AA              ^A^f^" 
ANY  DISTANCE  APART 

SIZE 

THICK- 
NESS 

LENGTH   OF  MEMBER   IN   FEET 

LENGTH   OF   MEMBER   IN   FEET 

3 

4 

6 

6 

7 

8 

9 

10 

11 

12 

13 

14 

IS 

16 

17 

18 

19 

20 

21 

8 

9 

10 

11 

12 

13 

14 

76 
72 
66 
60 
55 
49 
43 

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5x3 

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232* 
217* 
201* 
186* 
170* 
154* 
138* 
121* 
104* 

216* 
202* 
187* 
173* 
158* 
143* 
128* 
113* 
97* 

167* 
154* 
141* 
128* 
114* 
101* 
87* 
73* 

141* 

129* 
117* 
105 
92 
80 
67 

111 
101 
91 
80 
69* 
59* 

91 
82 
72 
63 
53 

75 
67 
58 
49 
39 

59 
51 
43 
35 

39 
33 
27 
21 

224* 
210* 
195* 
179* 
164 
148 
133 
117 
101 

208 
194 
180 
166 
152 
137 
123 
108 
93 

161 
148 
136 
123 
110 
97 
84 
70 

135 
123 
111 
100 
88 
76 
64 

106 
96 
87 
76 
66 
56 

86 
77 
68 
59 
50 

71 
63 
55 
46 
37 

55 
48 
40 
33 

36 
31 
25 
19 

216 
202 
188 
173 
158 
143 
128 
112 
97 

199 
186 
172 
159 
145 
131 
117 
103 
89 

154 
142 
130 
118 
105 
93 
80 
67 

128 
117 
106 
95 
83 
72 
60 

100 
91 
82 
73 
63 
53 

81 
72 
64 
56 

47 

67 
59 
51 
43 
35 

51 
44 
37 

30 

33 

28 
23 
17 

208 
195 
181 
166 
152 
138 
123 
108 
03 

191 
178 
165 
152 
138 
125 
112 
98 
85 

148 
136 
125 
113 
101 
89 
77 
64 

122 
111 
100 
90 
79 
68 
57 

95 
86 
78 
69 
60 
50 

75 
68 
60 
52 
44 

63 
55 
48 
41 
33 

47 
41 
34 
28 

29 
25 
20 
16 

200 
187 
174 
160 
146 
132 
118 
104 
89 

182 
170 
157 
145 
132 
119 
106 
94 
81 

142 
130 
119 
108 
96 
85 
73 
61 

115 
105 
95 
85 
75 
64 
54 

89 
82 
73 
65 
56 
48 

70 
63 
56 
49 
41 

58 
52 
45 
38 
31 

42 

37 
32 

26 

193 
180 
167 
154 
140 
127 
113 
99 
86 

173 
162 
150 
138 
125 
113 
101 
89 
76 

135 
124 
114 
103 
92 
81 
70 
58 

109 
99 
89 
80 
70 
60 
50 

84 
77 
69 
61 
53 
45 

65 

58 
52 
45 
38 

54 
48 
42 
35 
28 

185 
173 
160 
147 
134 
121 
109 
95 
82 

165 
154 
142 
131 
119 
107 
96 
84 
72 

129 
118 
108 
98 
87 
77 
66 
55 

102 
93 
84 
75 
66 
56 
47 

78 
72 
65 
57 
50 
42 

177 
165 
153 
141 
128 
116 
104 
91 
78 

156 
146 
134 
124 
112 
101 
90 
79 
68 

123 
113 
103 
93 
83 
73 
62 
52 

95 
87 
78 
70 
61 
52 
44 

73 
67 
60 
53 
46 
39 

180 

158 
146 
134 
122 
110 
99 
86 
74 

148 
138 
127 
117 
106 
95 
85 
75 
64 

116 
107 

97 
88 
78 
69 
59 
49 

161 
150 
139 
128 
116 
105 
94 
82 
71 

139 
130 
119 
110 

153 
143 

132 
122 
110 
100 
89 
78 
67 

146 
136 
125 

115 

138 
128 
118 
109 
98 
89 
79 
69 
59 

130 
121 
112 
102 
93 
84 
75 
65 
56 

122 
114 

114 
106 
98 
901 
81 
73 
65 
56 
48 

88 
82 
74 
68 

106 
99 
91 
83 
75 
67 
60 
52 
45 

99 
91 
84 
77 
69 
62 
55 
48 
41 

91 
84 

77 
70 

219 
206 
191 
176 
161 
146 
131 
116 
100 

200 
188 
175 
162 
148 
134 
121 
107 
92 

156 
144 
132 
121 
108 
95 
83 
69 

130 
119 
108 
97 
86 
74 
63 

104 

95 
85 
75 
65 
55 

88 
79 
70 
61 
51 

68 

60 
53 
45 
36 

55 
48 
41 
33 

36 
31 
25 

19 

207 
194 
180 
167 
153 
139 
124 
110 
95 

187 
175 
163 
151 
139 
126 
113 
100 
86 

146 
135 
124 
113 
101 
89 
78 
65 

119 
109 
99 
90 
79 
69 
58 

96 

88 
79 
70 
60 
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81 
73 
65 
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47 

62 
55 
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50 
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37 
30 

195 
183 
170 
157 
144 
131 
117 
104 
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173 
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151 
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129 
117 
105 
93 
80 

136 
126 
116 
105 
95 
84 
72 
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109 
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73 
63 
53 

88 
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64 
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183 

171 

160 
148 
135 
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160 
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119 
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97 
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126 
117 
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98 
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171 
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149 
138 
127 
115 
103 
91 
79 

146 
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119 
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99 
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116 

107 
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72 
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159 
149 
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us 

107 
96 
85 
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147 
137 
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109 
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79 
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134 
126 
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110 
100 
92 
83 
73 
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122 
115 

108 
100 
92 
84 
76 
67 
58 

110 
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97 
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61 
53 

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55 
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40 

66 
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57 
53 
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42 
37 
32. 

98 
92 
87 
81 
74 
68 
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105 
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52 

97 
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78 
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104 
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131 
122 
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65 
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114 
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69 
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114 
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105 
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85 
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41 
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132 
125 
116 

108 

119 

112 
104 
97 
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66 
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96 
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82 
75 
68 
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110 
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—  sT 

29 

57 
52 
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36 
32 
27 

42 
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60 
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60 

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42 
38 
33 
28 
23 

35 
31 
26 
21 

—  5T 

32 
28 
24 
20 

30 

27 
22 
18 

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27 

43 
36 
30 

45 

40 
33 

27 

38 
32 
26 

40 
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20 
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25 
22 
19 
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38 
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19 

23 
19 
16 

18 
15 
13 
10 

15 

12 

332 


TABLE  OF  SQUARES 


6 

z 

SQUARE! 

6 

z 

SQUARE! 

d 

z 

SQUARE! 

O 

z 

SQUARE! 

O 

z 

SQUARE 

O 

Z 

SQUARE! 

6 

z 

UJ 

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D 

cy 
to 

ci 

z 

SQUARE 

O 

z 

SQUARE 

6 

z 

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O 

z 

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ci 

z 

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O 

z 

SQUARE 

d 

z 

751 

SQUARE 

O 

z 

SQUARE! 

O 

z 

SQUARE 

d 

z 

SQUARE 

d 

z 

SQUARE 

101 

10201 

151 

22801 

201 

40401 

251 

63001 

301 

90601 

351 

123201 

401 

160S01 

451 

203401 

501 

251001 

551 

303601 

601 

361201 

651 

423801 

701 

491401 

.564001 

801 

641601 

851 

724201 

901 

811801 

951 

904401 

102 

10404 

152 

23104 

202 

40804 

252 

63504 

302 

91204 

352 

123904 

402 

161604 

452 

204304 

502 

252004 

552 

304704 

602  362404 

652 

425104 

702 

492804 

752 

565504 

802  6432U4 

852 

725904 

902 

813604 

952 

906304 

103 

10609 

153 

23409 

203 

41209 

253 

64009 

303 

91809 

353 

124609 

403 

162409 

453 

205209 

503 

253009 

553 

305809 

603  363609 

653 

426409 

703 

494209 

753 

567009 

803  644809 

853 

727609 

9T3 

815409 

9531  908209 

104 

10816 

154 

23716 

204 

41616 

254 

64516 

304 

92416 

354 

125316 

404 

163216 

454 

206116 

504 

254016 

554 

306916 

604 

364816 

654 

427716 

704 

495616 

751 

568516 

804 

646416 

854 

729316 

904 

817216 

954 

910116 

105 

11025 

155 

24025 

205 

42025 

255 

65025 

305 

93025 

355 

126025 

405 

164025 

455 

207025 

505 

255025 

555 

308025 

605 

366025 

655 

429025 

705 

497025 

755 

570025 

805 

648025 

855 

731025 

905 

819025 

955 

912025 

106 

11236 

156 

24336 

206 

42436 

256 

65536 

306 

93636 

356 

126736 

406 

164836 

456 

207036 

506 

256036 

556 

309136 

606 

367236 

656 

430336 

706 

498436 

756 

571536 

806 

649636 

856 

732736 

906 

820836 

956 

913936 

107 

11449 

157 

24649 

207 

42849 

257 

66049 

307 

94549 

357 

127449 

407 

165649 

457 

208849 

507 

257049 

557 

310249 

607 

368449 

657 

431649 

707 

499849 

757 

573049 

807 

651249 

857 

734449 

907 

822649 

957 

915849 

108 

11664 

158 

24964 

208 

43264 

258 

66564 

308 

94864 

35S 

128164 

408 

166464 

458 

209764 

508 

258064 

558 

311364 

608 

369664 

658 

432964 

70S 

501264 

758 

574564 

808 

652864 

858 

736164 

908 

824464 

958 

917764 

109 

11881 

159 

25281 

209 

43681 

259 

67081 

309 

95481 

359 

128881 

409 

167281 

459 

210681 

509 

259081 

559 

312481 

609 

370881 

659 

434281 

709 

502681 

759 

576081 

809 

654481 

859 

737881 

909 

826281 

959 

919681 

110 

12100 

160 

25600 

210 

44100 

260 

67600 

310 

96100 

360 

129600 

410 

168100 

460 

211600 

510 

260100 

560 

313600 

610 

372100 

660 

435600 

710 

504100 

760 

577600 

810 

656100 

860 

739600 

910 

828100 

960 

921600 

111 

12321 

161 

25921 

211 

44521 

261 

68121 

311 

96721 

361 

130321 

411 

168921 

461 

212521 

511 

261121 

561 

314721 

611 

373321 

661 

436921 

711 

505521 

761 

579121 

811 

657721 

861 

741321 

911 

829921 

961 

923521 

112 

12544 

162 

26244 

212 

44944 

262 

68644 

312 

97344 

362 

131044 

412 

169744 

462 

213444 

512 

262144 

562 

315844 

612 

374544 

662 

438244 

712 

506944 

762 

380644 

812 

659344 

X62 

743044 

912 

831744 

962 

925444 

113 

12769 

163 

26560 

213 

45369 

263 

69169 

313 

97969 

363 

131769 

413 

170569 

463 

214369 

513 

263169 

563 

316969 

613 

375769 

663 

439569 

713 

508369 

763 

582169 

813 

660969 

863 

744769 

913 

833569 

963 

927369 

114 

12996 

184 

26896 

214 

45796 

264 

69696 

31 

98596 

364 

132496 

414 

171396 

464 

215296 

514 

264196 

564 

318096 

614 

376996 

664 

440896 

714 

509796 

764 

583696 

814 

662596 

864 

746496 

914 

835396 

964 

929296 

115 

13225 

165 

27225 

215 

46225 

265 

70225 

315 

99225 

365 

133225 

415 

172225 

465 

216225 

515 

265225 

565 

319225 

615 

378225 

665 

442225 

715 

511225 

765 

585225 

815 

664225 

865 

748225 

915 

837225 

965 

931225 

116 

13456 

166 

27556 

216 

46656 

266 

70756 

316 

99856 

366 

133956 

416 

173056 

466 

£17156 

516 

266256 

566 

320356 

616 

379456 

666 

443556 

716 

512656 

766 

586756 

816 

665856 

866 

749956 

916 

839056 

966 

933156 

117 

13689 

167 

27889 

217 

47089 

267 

7  1289 

317 

100489 

367 

134689 

417 

173889 

467 

218089 

517 

267289 

567 

321489 

617 

380689 

667 

444S89 

717 

514089 

767 

588289 

817 

667489 

867 

751689 

917 

840889 

967 

935089 

118 

13924 

168 

28224 

218 

47524 

268 

71824 

318 

101124 

368 

135424 

418 

174724 

468 

219024 

518 

268324 

568 

322624 

618 

381924 

668 

446224 

718 

515524 

768 

589824 

818 

669124 

868 

(53424 

918 

842724 

968 

937024 

119 

14161 

169 

28561 

219 

47961 

269 

72361 

319 

101761 

369 

136161 

419 

175561 

469 

219961 

519 

269361 

569 

323761 

619 

383161 

669 

447561 

719 

516961 

769 

591361 

819 

670761 

869 

755161 

919 

844561 

969 

938961 

120 

14400 

170 

28900 

220 

48400 

270 

72900 

320 

102400 

370 

136900 

420 

176400 

470 

220900 

520 

270400 

570 

324900 

620 

384400 

670 

448900 

720 

518400 

770 

592900 

820 

672400 

870 

756900 

920 

846400 

970 

940900 

121 

14641 

171 

29241 

221 

48841 

271 

73441 

321 

103041 

371 

137641 

421 

177241 

471 

221841 

521 

271441 

571 

326041 

621 

385641 

671 

450241 

721 

519841 

771 

594441 

821 

674041 

871 

758641 

921 

848241 

971 

942841 

122 

14884 

172 

29584 

222 

49284 

272 

73984 

322 

103684 

372 

138384 

422 

178084 

472 

222784 

522 

272484 

572 

327184 

622 

386884 

672 

451584 

722 

521284 

772 

5C5984 

822 

675684 

872 

760384 

922 

850084 

972 

944784 

123 

15129 

173 

29929 

223 

49729 

273 

74529 

323 

104329 

373 

139129 

423 

178929 

473 

223729 

523 

273529 

573 

328329 

623 

388129 

673 

452929 

723 

522729 

773 

597529 

823 

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873 

762129 

923 

851929 

973 

946729 

124 

15376 

174 

30276 

224 

50176 

274 

75076 

324 

104976 

374 

139876 

424 

179776 

474 

224676 

524 

274576 

574 

329476 

624 

389376 

671 

454276 

724 

524176 

774 

599076 

824 

678976 

874 

763876 

924 

853776 

974 

948678 

125 

15625 

175 

30625 

225 

50625 

275 

75625 

325 

105625 

375 

140625 

425 

180625 

475 

225625 

525 

275625 

575 

330625 

625 

390625 

675 

455625 

725 

525625 

775 

600625 

825 

680625 

875 

765625 

925 

855625 

975 

950625 

128 

15876 

176 

30976 

226 

51076 

276 

76176 

326 

106276 

376 

141376 

426 

181476 

476 

226576 

526 

276676 

576 

331776 

626 

391876 

676 

456976 

726 

527076 

776 

602176 

826 

682276 

876 

767376 

926 

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976 

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127 

16129 

177 

31329 

227 

51529 

277 

76729 

327 

106929 

377 

112129 

427 

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227529 

527 

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577 

332929 

627 

393129 

677 

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727 

528529 

777 

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827 

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877 

769129 

927 

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977 

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128 

16384 

178 

31684 

228 

51984 

278 

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328 

107584 

378 

142884 

428 

183184 

478 

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528 

278784 

578 

334084 

628  394384 

678 

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728 

529984 

778 

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828 

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878 

770884 

928 

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978 

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129 

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179 

32041 

229 

52441 

279 

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329 

108241 

379 

143641 

429 

184041 

479 

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529 

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579 

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629  395641 

679 

461041 

729 

531441 

779 

6068-11 

829 

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879 

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929 

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979 

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130 

16900 

180 

32400 

230 

52900 

280 

78400 

330 

108900 

380 

144400 

430 

184900 

480 

230400 

£30 

280900 

580 

336400 

630 

396900 

680 

462400 

730 

532900 

780 

608400 

830 

688900 

880 

774400 

930 

864900 

980 

960400 

131 

17161 

181 

32761 

231 

53361 

281 

78961 

331 

109561 

381 

145161 

431 

185761 

481 

231361 

531 

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581 

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631 

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681 

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731 

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609961 

831 

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931 

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981 

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132 

17424 

182 

33124 

232 

53824 

282 

79524 

332 

110224 

382 

145924 

432 

186624 

482 

232324 

532 

283024 

582 

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632 

399424 

682 

465124 

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535824 

782 

611524 

832 

692224 

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777924 

932 

868624 

982 

964324 

133 

17689 

183 

33489 

233 

54289 

283 

80089 

333 

110889 

383 

146689 

433 

187489 

483 

233289 

533 

284089 

583 

339889 

633 

400689 

683 

466489 

733 

537289 

783 

613089 

833 

693889 

S83 

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933 

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983 

966289 

134 

17956 

184 

33856 

234 

54756 

284 

80656 

334 

111556 

384 

147456 

434 

188356 

484 

234256 

534 

285156 

584 

341056 

634 

401956 

6S4 

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734 

138756 

784 

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834 

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781456 

934 

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984 

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135 

18225 

185 

34225 

235 

55225 

285 

81225 

335 

112225 

385 

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435 

189225 

485 

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535 

286225 

585 

342225 

635 

403225 

an 

469225 

735 

540225 

785 

616225 

835 

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783225 

935 

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985 

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136 

18496 

186 

34596 

236 

55696 

286 

81796 

336 

112896 

386 

148996 

436 

190096 

48C 

236196 

536 

287296 

586 

343396 

636 

404496 

686 

470596 

736 

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786 

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836 

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886 

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936 

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137 

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187 

34969 

237 

56169 

287 

82369 

337 

113569 

387 

149769 

437 

190969 

487 

237169 

537 

288369 

587 

344569 

637 

405769 

687 

471969 

737 

543169 

787 

619369 

837 

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937 

877969 

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974169 

138 

19044 

188 

35344 

238 

56644 

288 

82944 

338 

114244 

388 

150544 

438 

191844 

488 

238144 

538 

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588 

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638 

407044 

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738  544644 

788 

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788544 

938 

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976144 

139 

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189 

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239 

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289 

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330 

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389 

151321 

439 

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489 

239121 

539 

290521 

589 

346921 

639 

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739 

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789 

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839 

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790321 

939 

881721 

989 

978121 

140 

19600 

190 

36100 

240 

57600 

290 

84100 

340 

115600 

390 

152100 

440 

193600 

490 

240100 

540 

291600 

590 

348100 

640 

409600 

690 

476100 

740 

547600 

790 

624100 

840 

705600 

890 

792100 

940 

883600 

990 

980100 

141 

19881 

191 

36481 

241 

58081 

291 

84681 

341 

116281 

391 

152881 

441 

194481 

491 

241081 

541 

292681 

591 

349281 

641 

410881 

691 

477481 

741 

549081 

791 

825681 

841 

707281 

891 

793881 

941 

885481 

991 

982081 

142 

20164 

192 

36864 

242 

58564 

292 

85264 

342 

116964 

392 

153664 

442 

195364 

492 

242064 

542 

293764 

592 

350464 

642 

412164 

692 

478864 

742 

550564 

792 

62/264 

842 

708964 

892 

795664 

942 

887364 

992 

984064 

143 

20449 

193 

37249 

243 

59049 

293 

85849 

343 

117649 

3!I3 

154449 

443 

196249 

493 

243049 

543 

294849 

593 

351649 

643 

413449 

693 

480249 

743 

552049 

793 

628849 

843 

710649 

893 

797449 

943 

889249 

993 

986049 

144 

20736 

194 

37636 

244 

59536 

294 

86436 

344 

118336 

394 

155236 

444 

197136 

494 

244036 

544 

295936 

594 

352836 

644 

414736 

694 

481636 

744 

553536 

794 

630436 

844 

712336 

894 

799236 

!)44 

891136 

994 

988036 

145 

21025 

195 

38025 

245 

60025 

295 

87025 

345 

119025 

395 

156025 

445 

198025 

495 

245025 

545 

297025 

595  354025 

645 

416025 

695 

483025 

715 

555025 

(95 

632025 

845 

714025 

895 

801025 

945 

893025 

995 

990025 

146 

21316 

196 

38416 

246 

60516 

296 

87616 

346 

119716 

396 

156816 

446 

198916 

496 

246016 

546 

298116 

59W  355216 

646 

417316 

6S6 

484U6 

746 

556516 

796 

633616 

846 

715716 

896 

802816 

946 

894916 

9% 

992016 

147 

21609 

197 

38809 

247 

61009 

297 

88209 

347 

120409 

397 

157609 

447 

199809 

4!<7 

247009 

547 

299209 

597 

356409 

647  418609 

697 

485809 

747 

558009 

797 

635209 

847 

717409 

897 

804609 

947  896809 

997 

994009 

148 

21904 

198 

39204 

248 

61504 

298 

88804 

348 

121104 

398 

158404 

448 

200V04 

498 

248004 

548 

300304 

598 

357604 

648:419904 

698 

487204 

748 

559504 

798 

636804 

848 

719104 

898 

W6404 

948  898704 

998 

996004 

149 

22201 

199 

39601 

249 

62001 

299 

89401 

349 

121801 

39!! 

159201 

449 

201601 

499 

249001 

549 

301401 

599358801 

W.I  421201 

699  488601 

749 

561001 

799 

638401 

849 

720801 

899 

S08201 

949  900601 

999 

998001 

150 

22500 

200 

40000 

250 

62500 

300 

90000 

350 

122500 

400 

160000 

450 

202500 

500 

250000 

550  302500 

600360000 

650  422500 

700  490000 

750 

562500 

800 

640000 

850 

722500 

900810000 

950  902500 

000 

1000000 

MOMENTS  OF  PINS  AND  DECIMAL  EQUIVALENTS 


333 


RESISTING  MOMENTS  OF  PINS  IN  POUND-INCHES 

DECIMAL  EQUIVALENTS 

DIAM. 

AREA 

UNIT    STRESS    FOR    EXTREME    FIBER    IN    POUNDS    PER    SQUARE    INCH 

DECIMALS   OF   A   FOOT 

DECIMALS 
OF   AN 

INS. 

SQ.  IN. 

15,000 

18,000 

20,000 

22,000 

22,500 

24,000 

25,000 

INS, 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

INCH 

Itt 

1  77 

4,970 

5.960 

6,630 

7,290 

7,460 

7,950 

8,280 

0 

.0000 

.0833 

.1667 

.2500 

.3333 

.4167 

.5000 

.5833 

.6667 

.7500 

.8333 

.9167 

1% 

2.07 

6,320 

7,580 

8,430 

9,270 

9,480 

10,100 

10,500 

V32 

.0026 

.0859 

.1693 

.2526 

.3359 

.4193 

.5026 

.5859 

.6693 

7526 

.8359 

.9193 

Hi 

.0313 

1% 
1% 

2.41 
2.76 

7,890 
9,710 

9,470 
11,600 

10,500 
12,900 

11,600 
14,200 

11,800 
14,600 

12,600 
15,500 

13,200 
16,200 

Me 

0052 

.0885 

.1719 

.2552 

.3385 

.4219 

.5052 

.5885 

.6719 

.7552 

.8385 

.9219 

Me 

.0625 

2 

3.14 

11,800 

14,100 

15,700 

17,300 

17,700 

18,900 

19,600 

%2 

.0078 

.0911 

.1745 

.2578 

.3411 

.4245 

.5078 

.5911 

.6745 

.7578 

.8411 

.9245 

%2 

.0938 

2Vs 

3.55 

14,100 

17,000 

18,800 

20,700 

21,200 

22,600 

23,600 

2Vi 

3.98 

16,800 

20,100 

22,400 

24,600 

25,200 

26,800 

28,000 

% 

.0104 

.0938 

.1771 

.2604 

.3438 

.4271 

.5104 

.5938 

.6771 

.7604 

.8438 

.9271 

H 

.1250 

2% 

4.43 

19,700 

23,700 

26,300 

28,900 

29,600 

31,600 

32,900 

%2 

.0130 

.0964 

.1797 

.2630 

.3464 

.4297 

.5130 

.5964 

.6797 

.7630 

.8464 

.9297 

%2 

.1563 

2'/2 

4.91 

23,000 

27,600 

30,700 

33,700 

34,500 

36,800 

38,300 

%6 

0156 

.0990 

.1823 

.2656 

.3490 

.4323 

.5156 

.5990 

.6823 

7656 

.8490 

.9323 

H« 

.1875 

2%    ' 

5.41 

26,600 

32,000 

35,500 

39,100 

40,000 

42,600 

44,400 

%» 

0182 

.1016 

.1849 

.2682 

.3516 

.4349 

.5182 

.6016 

.6849 

.7682 

.8516 

.9349 

%2 

.2188 

2% 

5.94 

30,600 

36,700 

40,800 

44,900 

45,900 

49,000 

61,000 

27/8 

6.49 

35,000 

42,000 

46,700 

51,300 

52,500 

56,000 

58,300 

Vi 

0208 

.1042 

.1875 

.2708 

.3542 

.4375 

.5208 

.6042 

.6875 

.7708 

.8542 

.9375 

Vi 

.2500 

3 

SVs 

7.07 
7.67 

39,800 
44,900 

47,700 
53,900 

53,000 
59,900 

58,300 
65,900 

59,600 
67,400 

63,600 
71,900 

66,300 
74,900 

%2 

0234 

.1068 

.1901 

.2734 

.3568 

.4401 

.5234 

.6068 

.6901 

.7734 

.8568 

.9401 

%2 

.2813 

8.30 

50,600 

60,700 

67,400 

74,100 

75,800 

80,900 

84,300 

H* 

0260 

.1094 

.1927 

.2760 

.3594 

.4427 

.5260 

.6094 

.6927 

.7760 

.8594 

.9427 

%e 

.3125 

3% 

8.95 

56,600 

67,900 

75,500 

83,000 

84,900 

90,600 

94,400 

'%2 

.0286 

.1120 

.1953 

.2786 

.3620 

.4453 

.5286 

.6120 

.6953 

.7786 

.8620 

.9453 

*%2 

.3438 

3V2 

9.62 

63,100 

75,800 

84,200 

92,600 

94,700 

101,000 

105,200 

3% 

10.32 

70,200 

84,200 

93,500 

102,900 

105,200 

112,200 

116,900 

% 

.0313 

.1146 

.1979 

.2813 

.3646 

.4479 

.5313 

.6146 

.6979 

7813 

.8646 

.9479 

% 

.3750 

3% 
3% 

11.05 
11.79 

77,700 
85,700 

93,200 
102,800 

103,500 
114,200 

113,900 
125,700 

116,500 
128,500 

124,300 
137,100 

129,400 
142,800 

%r 

0339 
.0365 

.1172 
.1198 

.2005 
.2031 

.2839 
.2865 

.3672 
.3698 

.4505 
.4531 

.5339 
.5365 

.6172 
.6198 

.7005 
.7031 

.7839 
.7865 

.8672 
.8698 

.9505 
.9531 

%!2 

.4063 
.4375 

4Vi 

12.57 
14  19 

94,200 
113,000 

113,100 
135,700 

125,700 
150,700 

138,200 
165,800 

141,400 
169,600 

150,800 
180,900 

157,100 
188,400 

»%2 

.0391 

.1224 

.2057 

2891 

.3724 

.4557 

.5391 

.6224 

.7057 

.7891 

.8724 

.9557 

>%2 

.4688 

4Vz 

15.90 

134,200 

161,000 

178,900 

196,800 

201,300 

214,700 

223,700 

4% 

17.72 

157,800 

189,400 

210,400 

231,500 

236,700 

252,500 

263,000 

Vi 

.0417 

.1250 

.2083 

.2917 

.3750 

.4583 

.5417 

.6250 

.7083 

.7917 

.8750 

.9583 

Vi 

.5000 

5 

19.64 

184,100 

220,900 

245,400 

270,000 

276,100 

294,500 

306,800 

17/32 

.0443 

.1276 

.2109 

.2943 

.3776 

.4609 

.5443 

.6276 

.7109 

7943 

.8776 

.9609 

l%2 

.5313 

SVi 

21.65 

213,100 

255.700 

284,100 

312,500 

319.600 

340.900 

355,200 

%6 

.0469 

.1302 

.2135 

.2969 

.3802 

.4635 

.5469 

.6302 

.7135 

7969 

.8802 

.9635 

%6 

.5625 

6% 

23.76 
25.97 

245,000 
280,000 

294,000 
336,000 

326,700 
373,300 

359,300 
410,600 

367,500 
419,900 

392,000 
447,900 

408.300 
466,600 

1%2 

.0495 

.1328 

.2161 

.2995 

.3828 

.4661 

.5495 

.6328 

.7161 

7996 

.8828 

.9661 

18/32 

.5938 

6 

28.27 

318,100 

381,700 

424,100 

466,500 

477,100 

508,900 

530,100 

6% 

30.68 

359,500 

431,400 

479,400 

527,300 

539,300 

575,200 

599,200 

% 

.0521 

.1354 

.2188 

.3021 

.3854 

.4688 

.5521 

6354 

.7188 

8021 

.8854 

.9688 

% 

.6250 

ttt 

33.18 

404,400 

485,300 

539,200 

593,100 

606,600 

647,100 

674,000 

2V32 

.0547 

.1380 

.2214 

.3047 

.3880 

.4714 

.5547 

.6380 

.7214 

8047 

.8880 

.9714 

2^2 

.6.563 

6% 

35  79 

452,900 

'543,500 

603,900 

664,300 

679,400 

724,600 

754,800 

JMe 

0573 

.1406 

.2240 

3073 

.3906 

.4740 

.5573 

.6406 

.7240 

8073 

.8906 

.9740 

JM6 

.6875 

7 

38.49 

505,100 

606,100 

673,500 

740,800 

757,700 

808,200 

841,800 

2%2 

.0599 

.1432 

.2266 

.3099 

.3932 

.4766 

.5599 

.6432 

.7266 

8099 

.8932 

.9766 

2%2 

.7188 

7*4 

41.28 

561.200 

673,400 

748,200 

823,100 

841,800 

897,900 

935,300 

lV"z 

44.18 

621,300 

745,500 

828,400 

911,200 

931,900 

994,000 

1,035,000 

7% 

47.17 

685,500 

822,600 

914,000 

1,005,000 

1,028,000 

1,097,000 

1,142,000 

% 

.0625 

.1458 

.2292 

.3125 

.3958 

.4792 

.5625 

.6458 

.7292 

8125 

.8958 

.9792 

% 

.7500 

8 

50  27 

754,000 

904,800 

1,005,000 

1,106.000 

1,131,000 

1,206,000 

1,257,000 

2%2 

.0651 

.1484 

.2318 

.3151 

.3984 

.4818 

.5651 

.6484 

.7318 

8151 

.8984 

.9818 

2%2 

.7813 

8Vi 

53.46 

826,900 

992,300 

1,103,000 

1,213,000 

1,240,000 

1,323,000 

1,378,000 

1?'l6 

0677 

.1510 

.2344 

.3177 

.4010 

.4844 

.5677 

.6510 

.7344 

8177 

.9010 

.9844 

J%6 

.8125 

8V2 

56.75 

904,400 

1,085,000 

1,206,000 

1,326,000 

1,357,000 

1.447,000 

1,507,000 

2%2 

.0703 

.1536 

.2370 

.3203 

.4036 

.4870 

.5703 

.6536 

.7370 

8203 

.9036 

.9870 

2%2 

.8438 

8% 

60.13 

986,500 

1,184,000 

1,315,000 

1,447,000 

1,480,000 

1,578,000 

1,644,000 

9 

9'  2 

63,62 
67.20 
70  88 

1,074,000 
1.166,000 
1,263,000 

1.288,000 
1,399,000 
1,515,000 

1,431,000 
1,554,000 
1,683,000 

1,575,000 
1,709,000 
1,852,000 

1.610,000 
1.748,000 
1,894,000 

1,718,000 
1,865,000 
2,020,000 

1,789,000 
1,943,000 
2,104,000 

2/%2 

.0729 
.0755 

.1563 
.1589 

.2396 
.2422 

.3229 
.3255 

.4063 
.4089 

.4896 
.4922 

.5729 
.5755 

.6563 
.6589 

.7396 
.7422 

8229 
8255 

.9063 
.9089 

.9896 
.9922 

i2 

.8750 
.9063 

9% 

74.66 

1,365,000 

1,638,000 

1,820,000 

2,002,000 

2,047,000 

2,184,000 

2,275,000 

15/i« 

.0781 

1615 

.2448 

.3281 

.4115 

.4948 

.5781 

.6615 

.7448 

8281 

.9115 

.9948 

a%6 

.9375 

10 

78.54 

1,473,000 

1,767,000 

1,963,000 

2,160,000 

2.209,000 

2,356,000 

2,454,000 

•fe 

0807 

.1641 

.2474 

.3307 

.4141 

.4974 

.5807 

.6641 

.7474 

8307 

.9141 

.9974 

•%. 

.9688 

334 


DESCRIPTION  OF  THE  TABLES  AND  DIAGRAMS 


DESCRIPTION   OF  THE  TABLES  AND  DIAGRAMS 


PAGE  298 


Weights  and  Dimensions  of  Carnegie  I-beams.  —  Some  of  these  beams 
rolled  by  the  Carnegie  Steel  Company  differ  from  those  tabulated  on  the 
opposite  page.  The  depth  in  inches  is  given  under  "Size,"  and  the  weight 
given  is  the  weight  per  linear  foot  of  beam.  The  weights  of  the  preferred 
beams  most  commonly  used  are  given  in  larger  type.  The  heavier  beams 
of  each  group  are  made  by  means  of  the  same  rolls,  but  the  rolls  are  sepa- 
rated. The  lighter  supplementary  beams,  indicated  by  asterisks,  are 
specially  designed  with  wider  flanges  and  thinner  webs  to  give  greater 
resistance  to  bending  in  proportion  to  then-  weights.  The  web  thicknesses 
are  given  in  both  decimal  and  fractional  forms.  The  flange  widths  and  the 
web  thicknesses  are  converted  into  fractions  upon  the  basis  noted  at  the 
top  of  the  table.  The  grip  t  is  the  thickness  of  the  flange  at  the  rivet  line 
located  by  the  standard  gage  g.  The  tangent  distance  between  the  curved 
fillets  may  be  found  by  subtracting  twice  the  distance  k  from  the  depth. 
The  standard  length  of  bearing  of  a  beam  on  a  masonry  wall  is  the  first 
dimension  (width)  of  the  corresponding  bearing  plate  found  hi  the  column 
headed  p. 

American  Bridge  Company  Connection  Angles.  —  The  numbers  of 
rivets  in  these  connection  angles  differ  from  those  in  the  angles  tabulated 
on  the  opposite  page,  but  they  have  been  tested  under  ordinary  condi- 
tions and  found  to  be  satisfactory.  A  constant  distance  of  5j"  between 
the  holes  in  the  outstanding  legs  is  used,  and  the  corresponding  gage  b 
varies  with  the  web  thickness.  A  single  6x6  angle  may  be  used  on  the 
lighter  beams  when  two  angles  cannot  be  used.  A  single  angle  should 
not  be  used  on  the  larger  beams  unless  specially  designed.  The  weights 
of  the  heads  of  the  f"  shop  rivets  are  included  in  the  weights  of  the  con- 
nection angles.  The  distance  c,  equal  to  one-half  the  web  thickness  plus 
TV,  may  be  used  to  advantage  in  determining  the  length  back  to  back  of 
angles  for  a  beam  which  is  supported  by  an  I-beam. 

PAGE   299 

Weights  and  Dimensions  of  Standard  I-beams.  —  Similar  to  the  tables 
described  above. 


Lackawanna  Connection  Angles.  —  These  connection  angles  are  simi- 
lar to  those  described  above.  The  numbers  and  the  spacing  of  the  rivets 
and  the  sizes  of  the  angles  differ.  A  gage  of  2j"  is  used  in  the  outstand- 
ing legs,  and  the  corresponding  distance  a  from  center  to  center  of  holes 
varies  with  the  web  thickness.  A  variable  gage  b  is  given  also  for  use 
with  a  constant  dimension  of  5j"  if  preferred. 

PAGE   300 

Weights  and  Dimensions  of  Carnegie  Channels.  —  Similar  to  the  table 
of  Carnegie  I-beams  described  above.  Dimensions  are  given  also  for 
spacing  the  channels  in  channel  columns.  Note  that  the  flange  faces  of 
the  webs  and  the  rivet  lines  are  both  kept  a  constant  distance  apart  for 
a  given  depth  of  channel,  but  the  gage  varies  with  the  web  thickness. 

American  Bridge  Company  Connection  Angles.  —  Similar  to  the  table 
of  American  Bridge  Company  connection  angles  for  I-beams  described 
above.  The  holes  are  symmetrical  about  the  center  of  the  web,  as  for 
I-beams.  There  is  an  additional  dimension  c'  equal  to  the  full  web  thick- 
ness plus  TV". 

PAGE  301 

Weights  and  Dimensions  of  Standard  Channels.  —  Similar  to  the  table 
of  Carnegie  channels  described  above. 

Lackawanna  Connection  Angles.  —  Similar  to  the  table  of  Lackawanna 
connection  angles  for  I-beams  described  above.  A  distance  h  from  the 
back  of  the  channel  to  the  holes  in  the  angles  is  shown,  and  also  a  dimen- 
sion c'  equal  to  the  full  web  thickness  plus  TV". 

- 

PAGE   302 

Weights  and  Dimensions  of  Bethlehem  I-beams  and  Girder  Beams.  — 

The  left  half  of  the  table  shows  the  special  I-beams  rolled  by  the  Bethle- 
hem Steel  Company,  and  the  right  half  the  girder  beams  rolled  by  the 
same  company.  The  dimensions  are  tabulated  as  in  the  preceding  tables. 
Bethlehem  Connection  Angles.  —  These  connection  angles  are  arranged 
as  in  the  preceding  tables. 


DESCRIPTION   OF  THE  TABLES  AND   DIAGRAMS 


335 


PAGE  303 

Weights  and  Areas  of  Angles.  —  The  weights  per  linear  foot  and  the 
areas  of  cross  section  in  square  inches  are  tabulated  for  standard  angles 
at  the  left  and  for  special  angles  at  the  right.  This  arrangement  simpli- 
fies the  selection  of  a  standard  angle  to  fulfill  requirements. 

Gages  of  Angles.  —  The  standard  gages  commonly  used  for  different 
sizes  of  angles. 

Areas  of  Rivet  Holes.  —  This  table  gives  the  areas  of  cross  section 
(rectangles)  of  holes  of  different  diameters  in  metal  of  different  thick- 
nesses. Note  that  the  diameter  of  the  hole  is  taken  1"  greater  than  the 
nominal  diameter  of  the  corresponding  rivet. 

PAGE  304 

Weights  and  Dimensions  of  Rivets  and  Bolts.  —  These  tables  are  self- 
explanatory. 

Rivet  Code.  —  The  inner  rows  show  the  conventional  method  of  indi- 
cating rivets  with  different  forms  of  heads.  The  outer  rows  represent 
the  corresponding  rivets. 

Clearance  for  Machine-driven  Rivets.  —  This  shows  the  desired  dis- 
tance and  the  minimum  distance  from  the  center  of  a  rivet  to  any  pro- 
jecting part  which  might  interfere  with  the  use  of  a  riveting  machine. 

Minimum  Rivet  Stagger.  —  This  shows  the  minimum  stagger  of  rivets, 
in  opposite  legs  of  an  angle,  which  will  provide  the  driving  clearance  tabu- 
lated at  the  left  of  the  page. 

PAGE  306 

Minimum  Rivet  Spacing.  —  This  shows  the  minimum  spaces  used  for 
ordinary  work.  The  minimum  pitches  in  the  flanges  of  plate  girders  are 
shown  in  the  table  on  the  following  page. 

Maximum  Rivet  Spacing.  —  This  shows  the  maximum  spaces  under 
ordinary  conditions. 

Edge  Distance.  —  This  shows  the  minimum  and  maximum  values  for 
the  perpendicular  distance  from  the  center  of  a  rivet  to  the  sheared  edge 
of  any  piece.  The  distance  to  a  rolled  edge  may  be  less  necessarily. 

Minimum  Rivet  Stagger.  —  There  are  two  sets  of  curves  for  determin- 
ing the  minimum  stagger  of  rivets.  The  circular  curves  show  when  the 


diagonal  distance  from  center  to  center  of  holes  equals  the  usual  mini- 
mum given  in  the  table  at  the  top  of  the  page.  The  other  curves  show 
how  close  together  two  rivets  may  be  placed  in  a  tension  member  with- 
out the  necessity  of  considering  both  in  finding  the  limiting  net  cross 
section,  as  explained  more  fully  on  page  209  : 1.  This  diagram  can  be 
used  even  when  the  holes  are  in  different  legs  of  an  angle,  as  indicated 
below  the  diagram.  For  the  minimum  stagger  for  the  rivets  in  the  flanges 
of  plate  girders,  see  the  following  table. 

PAGE  306 

Minimum  Pitches  for  Flange  Rivets.  —  These  tables  give  the  minimum 
pitches  for  the  rivets  in  the  flanges  of  plate  girders  under  different  con- 
ditions. Their  importance  and  their  use  are  described  more  fully  on  page 
255  : 2.  The  upper  table  should  be  used  to  conform  to  the  specifications 
of  the  American  Railway  Engineering  Association. 

PAGE  307 

Multiplication  Table  for  Rivet  Spacing.  —  This  table  is  self-explanatory. 
Values  for  pitches  in  sixteenths  can  be  interpolated  or  found  by  taking 
one-half  the  values  which  correspond  to  pitches  twice  as  large. 

PAGES  308  TO   311 

Rivet  Values.  —  These  four  tables  are  practically  self-explanatory,  but 
they  are  described  on  page  231  : 1. 

PAGE  312 

Graphic  Resultants  —  Decimals.  This  diagram  may  be  used  to  ad- 
vantage in  finding  the  resultants  of  forces  or  stresses  in  pounds  or  in 
thousands  of  pounds.  One  component  is  measured  horizontally,  the 
other  vertically,  while  the  resultant  is  measured  diagonally.  There  are 
five  spaces  between  numbers,  the  odd  tenths  falling  in  the  centers  of  the 
spaces.  The  diagram  can  often  be  used  to  better  advantage  if  both  com- 
ponents are  multiplied  or  divided  by  a  convenient  factor,  and  the  result- 
ant corrected  to  correspond. 


336 


DESCRIPTION   OF  THE  TABLES  AND   DIAGRAMS 


PAGE   313 

Graphic  Resultants  —  Inches  and  Fractions.  This  diagram  may  be 
used  to  advantage  in  finding  small  diagonal  distances  in  inches  and  frac- 
tions from  rectangular  coordinates,  in  much  the  same  manner  as  in  the 
preceding  diagram.  There  are  eight  spaces  between  numbers,  the  six- 
teenths 'being  interpolated. 

PAGE  314 

Graphic  Resultants  —  Feet  and  Inches.  This  diagram  may  be  used 
in  finding  diagonal  distances  in  feet  and  inches  from  rectangular  coordi- 
nates, in  the  same  manner  as  in  the  two  preceding  diagrams.  There  are 
six  spaces  between  numbers,  the  inches  being  interpolated.  This  diagram 
cannot  be  expected  to  replace  a  table  of  squares  in  computing  lengths  of 
diagonals  to  the  nearest  sixteenths  of  an  inch,  but  it  can  be  used  for  less 
precise  work. 

PAGE  315 

Purlin  Connections.  —  Typical  standard  purlin  connections  to  roof 
trusses  or  rafters  are  here  shown  in  detail.  The  .angles  are  usually  ^" 
thick. 

Lattice  Bars.  —  The  maximum  lengths  of  lattice  bars  for  different 
thicknesses  are  shown  for  different  specifications.  The  values  given  in 
the  left-hand  columns  for  both  single  and  double  latticing  correspond  to 
the  more  usual  specifications.  The  detailed  dimensions  at  the  ends  of 
lattice  bars  are  shown  also. 

Areas  and  Weights  of  Rods.  —  The  gross  areas  of  round  rods,  and  the 
diameters  and  the  lengths  of  standard  upset  ends  are  given.  The  areas 
at  the  roots  of  the  threads  of  the  upset  ends  are  shown.  These  root  areas 
may  be  used  also  for  rods  which  are  not  upset,  intermediate  values  being 
tabulated  on  page  207  : 4. 

PAGE  316 

Bearing  Plates.  —  The  relation  between  the  thickness  of  a  bearing 
plate  and  its  projection  beyond  the  superimposed  metal  is  shown  in  the 
diagram.  The  unit  stress  in  bending  in  the  extreme  fiber  of  the  steel 
plate  is  16,000#/sq.  in.,  but  different  lines  indicate  different  bearing  values 
allowed  on  the  masonry.  If  the  projection  is  known,  the  required  thick- 
ness may  be  determined  by  the  vertical  distance  to  the  intersection  of 


the  proper  vertical  and  diagonal  lines.    Conversely,  the  maximum  projec- 
tion of  a  plate  of  a  given  thickness  may  be  found. 

Separators.  —  Detailed  dimensions  of  cast-iron  separators  for  I-beam 
girders  of  different  sizes  are  shown,  and  the  weights  of  the  separators  and 
the  bolts  used  with  them  are  given. 

Anchors.  —  Details  are  shown  of  Government  anchors  and  angle 
anchors  for  beams,  and  of  swedge  bolts  and  built-in  anchor  bolts  for 
other  classes  of  work. 

Rod  Connections.  —  Different  methods  are  indicated  for  attaching 
rods  to  other  members.  Details  are  given  for  the  ends  of  tie  rods  or  sag 
rods. 

PAGE  317 

Dimensions  and  Properties  of  Rails.  —  Detailed  dimensions,  areas, 
and  section  moduli  of  rails  of  different  weights  per  yard  are  shown  for 
the  different  standards  (page  44:7). 

Rail  Fastenings.  —  Details  are  given  for  the  splice  bars  for  crane  rails, 
with  punching  to  match  the  standard  mill  punching  at  the  ends  of  the 
rails.  Hook  bolts  for  fastening  crane  rails  to  the  tops  of  I-beams,  rail 
clamps  for  fastening  crane  rails  to  the  tops  of  plate  girders,  and  crane 
stops  to  be  bolted  to  the  ends  of  crane  rails  are  illustrated. 

Unit  Stresses  for  Structural  Steel.  —  These  are  self-explanatory. 

PAGE  318 

Shear  and  Moment  Table  for  Cooper's  Engine  Loading.  —  This  table 
is  largely  self-explanatory,  but  its  use  is  more  fully  described  on  page 

193:1. 

PAGE   319 

Properties  of  Wooden  Rectangular  Beams.  —  This  table  shows  the 
section  moduli  for  rectangular  beams,  not  only  for  nominal  dimensions 
in  even  inches,  but  also  for  dimensions  which  conform  to  the  actual  sizes 
of  sawed  and  planed  lumber.  The  designer  should  be  familiar  with  the 
practice  of  the  lumber  mills  which  furnish  the  wooden  beams  for  any 
structure  which  he  designs,  and  he  should  use  the  sizes  which  are  likely 
to  be  delivered.  The  table  shows  also  the  area  of  cross  section,  the  num- 
ber of  feet-board  measure  per  foot  of  length,  and  the  weight  per  linear 
foot  for  each  section. 


DESCRIPTION   OF  THE  TABLES  AND   DIAGRAMS 


337 


PAGE  320 

Unit  Stresses  for  Structural  Timber.  —  The  unit  stresses  are  given  for 
different  kinds  of  structural  timber,  and  for  different  types  of  structure, 
as  clearly  indicated  in  the  table. 

Moments  of  Inertia  of  Rectangles.  —  These  moments  of  inertia  are 
for  rectangles  in  which  the  longer  dimension  is  at  right  angles  to  the  neu- 
tral axis  through  the  center.  Moments  of  inertia  of  rectangles  wider 
than  1  inch  can  be  found  by  multiplying  the  values  in  the  last  column 
by  the  widths  in  inches. 

PAGE   321 

Areas  of  Plates.  —  The  areas  of  plates  most  likely  to  be  used  are  in- 
cluded in  the  table;  others  may  be  found  by  interpolation  or  by  propor- 
tion. Note  the  inset  portion  which  shows  the  areas  of  the  wider  plates. 
The  net  areas  of  cover  plates  or  similar  plates  may  be  found  from  the 
table  by  using  the  net  widths  of  the  plates.  These  are  found  by  deduct- 
ing from  the  full  widths  the  diameters  of  the  rivet  holes  cut  by  any  one 
section. 

Weights  of  Plates.  —  The  weights  per  linear  foot  are  given  for  steel 
plates  of  different  cross  section.  Note  the  inset  portion  for  the  weights 
of  the  wider  plates. 

PAGE  322 

Properties  of  I-beams.  —  This  table  is  self-explanatory.  The  I-beams 
are  placed  in  two  groups  to  correspond  to  those  on  pages  298  and  299. 
The  web  thicknesses  are  converted  to  fractions  upon  a  different  basis 
from  that  used  in  the  first  five  tables,  some  of  resulting  values  used  in 
designing  being  TV  less  than  the  corresponding  values  used  in  drafting. 

PAGE  323 

Properties  of  Channels.  —  This  table  is  self-explanatory.  See  note 
regarding  web  thicknesses  in  the  preceding  paragraph. 

PAGE  324 

Properties  of  Bethlehem  I-beams  and  Girder  Beams.  —  These  tables 
are  self-explanatory.  See  note  regarding  web  thickness  under  "  Properties 
of  I-beams  "  above, 


List  of  Shipping  Marks.  —  If  further  explanation  is  necessary,  see 
Chapter  XVI,  page  79. 

PAGES  326  AND   326 

Properties  of  Standard  and  Special  Angles.  —  For  convenience,  the 
properties  of  standard  angles  and  special  angles  are  placed  on  different 
pages.  7s,  «s,  and  rs  represent  respectively  the  moment  of  inertia,  the 
section  modulus,  and  the  radius  of  gyration  about  the  axis  through  the 
center  of  gravity  parallel  to  the  shorter  (or  equal)  leg,  and  x  is  the  distance 
from  the  back  of  this  leg  to  this  axis.  IL,  SL  and  TL  represent  the  moment 
of  inertia,  the  section  modulus,  and  the  radius  of  gyration  about  the  axis 
through  the  center  of  gravity  parallel  to  the  longer  leg,  and  y  is  the  dis- 
tance from  the  back  of  this  leg  to  this  axis,  m  is  the  minimum  or  least 
radius  of  gyration  which  is  about  a  diagonal  axis. 

PAGE  327 

Two  Angles  in  Tension.  —  This  table  may  be  used  to  advantage  in 
designing  plate  girders  as  well  as  two-angle  tension  members.  The  ten- 
sile stresses  are  used  when  the  unit  stress  is  16,000#/sq.  in.  The  net  areas 
are  used  for  other  unit  stresses. 

PAGE  328 

Unit  Stresses  for  Compression.  —  This  table  gives  the  resulting  unit 
stresses  found  by  substituting  different  values  for  the  length  and  the 
radius  of  gyration  in  the  common  column  formula  printed  at  the  top  of 
the  table.  A  maximum  of  14,000  is  usually  specified,  and  if  so,  it  should 
be  used  in  place  of  the  values  below  the  dotted  lines  in  the  lower  left-hand 
portion  of  the  table.  The  maximum  ratio  of  slenderness  for  the  main- 
compression  members  of  bridges  is  usually  specified  as  100,  while  for 
buildings  125  is  allowed.  The  maximum  for  secondary  compression 
members  is  usually  120  for  bridges  and  150  for  buildings.  Zigzag  lines 
are  used  to  indicate  these  ratios. 

PAGE  329 

Radii  of  Gyration  of  Two  Angle  Struts.  —  The  radii  of  gyration  are 
given  about  axes  parallel  to  both  legs  through  the  center  of  gravity  of 
compression  members  composed  of  two  angles  spaced  at  different  dis- 


338 


DESCRIPTION  OF  THE  TABLES  AND  DIAGRAMS 


tances  apart.  This  table  can  be  used  to  advantage  in  designing  compres- 
sion members  for  other  unit  stresses  from  that  used  in  the  following 
tables. 

PAGES  330  AND   331 

Safe  loads  of  Single  Angle  and  Two  Angle  Struts.  —  These  tables  show 
the  maximum  total  loads  which  can  be  placed  upon  compression  mem- 
bers composed  of  one  or  two  angles  of  different  lengths  without  exceeding 
the  unit  stress  shown  at  the  tops  of  the  tables.  The  zigzag  lines  indicate 
the  limiting  ratios  for  different  types  of  members,  as  described  above. 

PAGE  332 

Table  of  Squares.  —  This  table  is  self-explanatory.  The  square  of  a 
number  less  than  100  can  be  found  from  the  table  by  moving  the  decimal 


point  of  the  number  one  place  and  that  of  the  corresponding  square  two 
places.    Similarly,  the  squares  of  numbers  over  1000  can  be  found. 

PAGE  333 

Resisting  Moments  of  Pins.  —  This  table  gives  the  resisting  moments 
of  cylindrical  pins  for  different  unit  stresses. 

Decimal  Equivalents.  —  This  table  may  be  used  to  convert  dimensions 
in  inches  and  fractions  of  inches  to  the  corresponding  decimals  of  a  foot, 
and  conversely.  It  may  also  be  used  to  convert  fractions  of  an  inch  to 
decimals  of  an  inch,  and  vice  versa. 


INDEX 


(For  definitions  of  engineering  terms,  see  pages  6  to  18.     For  description  of  tables  and  diagrams,  see  pages  334  to  338.) 
Page  numbers  are  usually  followed  by  one  or  more  paragraph  numbers,  for  example,  255:2  or  255:1,  2 


ABBREVIATIONS,  6,  45:7,  48:5 
ACCURACY, 

in  designing,  220:2 
in  plotting,  35:2 

ACTUAL   SHAPES    of    cross    sec- 
tions, 26:1 

AMBIGUITY   avoided   in   dimen- 
sions, 47:4 
ANCHOR  for  beams,  88:2,  174:1, 

316 

ANCHOR  BOLTS,  174:1 
for  columns,  134:4 
for  girders,  106:5 
holes  for,  73:3 
plan  of,  152:1,  3 
ANGLE,   ANGLES, 
actual  shape,  26:1 
areas,  table,  303 
bent,  78:1 
connection,  83:6 
design,  86:  3 
different  depths  of  beams, 

86:2 

methods  of  detailing,  84:1,  2 
single,  86:1 
tables,  298-302  incl. 
cover,  274:2 

flange,  in  plate  girders,  219:2 
four  in  each  flange,  227:1 
splice,  274:2 

gages,     68:5,     106:3,     132:3, 
136:1,  139:3;  table,  303 


ANGLE,  ANGLES  (Continued) 

how  billed,  44:1 

how  expressed,  50:7 

how  shown,  38:6 

net  areas,  table,  327 

not  expressed  in  degrees,  50:7 

ordering  from  mill,  165:1 

properties  of  special,  table,  326 

properties  of  standard,  table, 
325 

reentrant,  29:3,  123:6,  141:4 

seat,  73:2 

ekewback,  94:3 

splice,  274:2 

stiffening,  see  "stiffenere" 

tensile  strength,  table,  327 

thickness  in  compression,  212 :2 

top,  89:2 

weights,  table,  303 
ANGLE  ANCHORS,  316 
ANGLE  SHEARS,  28:1 
ANGLE  STRUTS, 

radii  of  gyration,  table,  329 

safe  loads,  tables,  330,  331 
ANNEALING,  31:6 
APPEARANCE  of  drawing,  55:1 
APPLICATION  of  forces  on  pins, 

278:3 

ARCHITECTS'  SCALE,  35:3 
AREA,  AREAS, 

angles,  table,  303 

Bethlehem  beams,  table,  324 


AREA,  AREAS  (Continued) 

channels,  table,  323 

cross  section,  206:3 

flanges  of  girders,  219:4 

holes,  208:2,  table,  303 

I-beams,  table,  322 

net,  see  "net  area" 

plates,  table,  321 

rivet  holes,  table,  303 

rods,  table,  315 

root  of  thread,  table,  315 
ARRANGEMENT, 

computation,  185:1,  208:3 

drawings,  34:3, 115:1, 121:2,  3, 
131:2,  138:5 

order  bills,  163:4 

shop  bills,  167:4 

this  book,  1 :2 
ARROW  HEADS, 

how  made,  47:4 

inking,  60:3 
ASSEMBLING,  30:3 
ASSEMBLING  MARKS,  79:2 

component  parts,  79:4 
first  letter,  80:1 
second  letter,  80:2 
sheet  number,  80:3 

rights  and  lefts,  80:4 

summary,  80:5 

when  used,  79:3 

ASSISTANT     CHIEF     ENGINEER, 
20:2 

339 


ASSUMPTIONS, 
girder  design,  221:1,  223:1 
riveted  connections,  228:4 

AUXILIARY     WORKING     LINES, 
77:1,  108:5 

BACK  CHECKING,  182:1 
BALL-POINTED  PEN,  57:3 
BALTIMORE  TRUSS, 
bridge,  120:2 
roof,  113:2 
BAH,  see  "eye  bar"  or  "lattice 

bar" 
BASE, 

cast-iron,  290:1 
column,  134:4,  174:3,  290:1 
BASE  PLATE,  134:4,  290:1 
BATTEN  PLATE, 
size,  216:2 
use,  208:1,  212:2 
BEAM,  BEAMS, 
anchors,  88:2 
bearing,  203:1 
bearing   plates,   88:2;   tables, 

316 
bending  moment,  see  "bending 

moment" 
cantilever,  83:1 

bending  moment,  see  "bend- 
ing moment" 
shear,  see  "shear" 
common  forms,  83:3 


BEAM,  BEAMS  (Continued) 

connection  angles,  83:6 
design,  86:3,  234:2 
different  depths  of  beams, 

86:2 

methods  of  detailing,  84:1,  2 
single-angle,  86:1 
tables,  298-302  incl. 

continuous,  83:1,  192:4 

coping,  29:3,  89:1 

crane-runway,  94:4 

cylindrical,  200:1 

deflection,  203:2 

design, 

bearing,  203:1 
bending,  197:3,  198:1 . 
buckling,  293:3 
cylindrical,  200:1 
effect  of  bending,  197:3 
effect  of  holes,  201:1 
lateral  supports,  201:2 
lateral  thrust,  201 :3 
points  considered,  197:1,  2 
rectangular,  199:3 
resisting  moment,  198:1 
section  modulus,  199:1 
shear  intensity,  202:1 
steel,  200:2 
units,  199:2 
unit  stress,  198:2 
weight  assumed,  200:3 
wooden,  199:3 


340 


INDEX 


BEAM,  BEAMS  (Continued) 

diagonal  cuts,  94:5 

dimensions,  table,  298-302 

extension  figures,  86:5 

grillage,  see  "grillage  beams" 

horizontal  dimensions,  86:5 

length,  86:6 

longitudinal  shear,  202:1 

mill  variation,  25:2,  88:1 

office-building,  89:2 

ordered  length,  88:1 

ordering  from  mill,  164:7 

printed  forms,  83:4 

properties,  tables 
Bethlehem,  324 
channels,  323 
I-beams,  322 
rectangular,  319 

restrained,  192:4 

seat  angles,  73:2,  89:2,  235:1 

segment,  183:4,  184:4 

shear,  see  "shear" 

shear  intensity,  202:1 

shown  full  length,  86:4 

simple,  83:1 

bending  moment,  see  "bend- 
ing moment" 

shear,  see  "shear" 

skew  connections,  94:5 

supports,  83:5 

tie  rods,  holes,  90:2 

top  angles,  89:2 

vertical  dimensions,  84:2 

wall  bearing,  88:2 

web  connections,  83:6,  234:2 

weight,  tables,  298-302  incl., 

319 

BEAM  BEVEL,  38:7 
BEAM  CONNECTIONS  on  columns, 

132:3 

BEAM  GIRDERS,  91:5 
BEAM  PUNCH,  multiple,  91 :2 
BEAM  SEPARATORS^  table,  316 


BEAM  SHEARS,  28:1 
BEARING, 

beams,  design,  203:1 
pins,  284:4 

reinforcing  plates,  284:4 
rivets,  230:3 
soil,  292:3 
stiff eners,  267:1 
BEARING  PLATES, 
beams,  88:2,  174:1 
diagram,  316 
double,  289:2 
size,  288:2 
tables,  316 
thickness,  288:3 
type,  288:1 
BEARING  VALUES  of  rivets  and 

bolts,  tables,  308-311  incl. 
BENDING, 

beams,  197:3,  198:1 
pins,  279:1 
rivets,  228:4 
unit  stress,  198:2 
BENDING  MOMENTS,  183:1 
arrangement  of  computation, 

185:1 

combined  loads,  188:1,  192:2 
concentrated  loads,  186:1 
continuous  beams,  192:4 
Cooper's  loading,  193:1,  195:1, 

196:1 

diagram,  318 
definition,  184:2 
forces  considered,  183:4 
formulas,  184:3 
live    and    dead    load,    simple 

beam,  192:2 
live  concentrated  load,  simple 

bsam,  191:1 
live     uniform     load,     simple 

beam,  190:2 
live    load,    cantilever    beam, 

192:3 


BENDING  MOMENTS  (Continued) 

maximum  on  pins,  280:1 

principles,  183:2 

reactions,  185:2 

relation  to  shear,  189:1 

restrained  beams,  192:4 

short-cut  rule,  188:2 

signs,  6,  183:3 

sketches,  184:4 

through  girders,  196:2 

uniform  loads,  187:1,  188:2 

units,  3:2,  184:2 
BENT  ANGLES,  78:1 
BENT  PLATES, 

how  shown,  41 :4 

layout,  78:1 
BENZINE,  use,  64:1 
BESSEMER  STEEL,  23:2 
BETHLEHEM  BEAMS, 

dimensions,  table,  302 

properties,  table,  324 

weights,  table,  302 
BEVEL, 

beam,  38:7 

calculation,  76:2 

dimensioning,  50:7 
BEVELED  WASHER,  316 
BILLS,  see  "order  bills,"  "ship- 
ping bills, "  or  "  shop  bills. " 
BILLERS,  20:4 
BILLING,  43:1 

conventional  signs,  43:2 

when  inked,  60:5 
BINS,  146:5 
BLACK  INK,  36:2,  58:1 
BLAST  FURNACE,  23:1 
BLOCKING  OUT,  29:3,  89:1 
BLOOM,  23:3 
BLOOMING  MILL,  23:3 
BLOTTER,  59:8 
BOARD  MEASURE,  200:3 
BOLTS, 

anchor,  174:1 


BOLTS  (Continued) 

dimensions,  table,  304 

erection,  178:1 

erector's  list,  176:2 

field,  list,  176:2 

grip,  176:2 

how  billed,  45:5 

how  made,  31 :6 

how  shown,  41:2 

length,  176:2 

list,  176:2 

number,  177:1 

permanent,  53:3 

shipment,  53:2 

spiking  pieces,  91 :3 

summary,  177:1 

swedge,  316 

table,  304 

temporary,  53:2 

unit  stress,  230:4 

use  of,  230:4 

values,  tables,  308-311  incl. 

weight,  170:1 
BORDER,  54 :6,  7 

when  inked,  61:1 
BORING,  31:2 
BORING  MACHINE,  31:2 
BOTTOM-CHORD  BRACING,  119:3, 

139:6 
BOTTOM  LATERAL  BRACING, 

141:3 

BOTTOM  SECTIONAL  VIEW,  34:1 
Box  GIRDERS,  94:1,  107:2,  252:1 
BRACING,  cross,  138:5 
BRACING  DIAGONALS,  139:1 
BRACING  RODS,  119:2 
BRACING  SYSTEMS, 

arrangement,  138:5 

bottom  chord,  buildings,  139:6 

bottom  lateral,  bridges,  141:3 

brackets,  144:1 

connections,  119:2,  3,  139:2 

considered  as  trusses,  138:2 


BRACING  SYSTEMS  (Continued) 

cross,  138:5 

cross  frames,  144:2 

diagonal,  138:1,  5,  145:1 

gages  in  angles,  139:3 

initial  tension,  139:1 

knee  braces,  141:2,  145:1 

mill  buildings,  139:5 

office  buildings,  145:1 

portal,  141:4,  145:1 

statically  complete,  138:3 

top  lateral,  bridges,  141 :4 

types,  138:1 

unsymmetrical,  141:1 

working  lines,  138:4,  5,  139* 
BRACKETS,  144:1,  145:1 
BREAKS,  how  shown,  38:1 
BRIDGE  DIAGRAMS,  152:1,  2 
BRIDGE  TRUSSES, 

arrangement  on  sheet,  121:2 

arrangement  of  views,  121:3 

camber,  123:2 

collision  struts,  120:2 

Cooper's  engine  loading,  196:3 

counters,  120:2 

method  of  holding  in  place, 
130:5 

countersunk  rivets,  130  2 

clearance,  130:4 

deck,  120:2 

deflection,  123:2 

flattened  rivets,  130:2 

milling,  123:5 

pony,  144:1 

protection  from  weather,  130:3 

reinforcing  plates,  130:1 

shipping  marks,  82:1,  123:1 

sizes  of  pin  holes,  123:3 

splices,  123:6 

through,  120:2 

types,  120:2 

types  of  members,  123 :4 

when  used,  120:1 


INDEX 


341 


BRIDGE  TRUSSES  (Continued) 

working  lines,  121:3 
BRUSH,  use,  63:5 
BUCKLING,  beams,  293:3 

CALCULATED  WEIGHTS,  170:1 
CALCULATION  of  slopes,  76:2 
CALKING,  146:4 
CAMBER,  107:3,  123:2 
CAMEL-BACK  TRUSS,  120:2 
CANTILEVER  BEAMS,  83:1 

bending  moment,  see  "bend- 
ing moment" 

flange  rivets,  252:2 

shear,  see  "shear." 
CANTILEVER  GIRDERS  in  founda- 
tions, 292:4 

CARBON  in  iron  and  steel,  23:1,  2 
CARDBOARD  TEMPLETS,  27:5 
CAHE  of  tracing  cloth,  55:3 
CASTINGS,  174:1 
CAST-IKON  BASES,  174:3 
CAST-IRON  PEDESTALS,  289:3 
CAST-IRON     SEPARATORS,    91 :5, 

table,  316 
CENTER    HANGER,    roof    truss, 

118:3 
CENTER  OF  GRAVITY, 

compression  member,  212:1 

eccentric   connections,   237 :3, 
238:1 

girder  flange,  224:1 
CENTER  OF  ROTATION,  237:3 
CENTER  PUNCH,  27:5,  29:2 
CENTRIFUGAL  FORCES,  227 :2 
CHALK,  on  tracing  cloth,  56:2 
CHAMFERING,  29:4 
CHANGE    ORDERS    or    CHANGE 

SLIPS,  164:5 
CHANNEL,  CHANNELS, 

actual  shape,  26:1 

areas,  table,  323 

coping,  29:3,  89:1 


CHANNEL,  CHANNELS  (Cont'd) 

design,  200:2 

dimensions,  tables,  300,  301 

gages,    68:5,     132:1;     tables, 
300,  301 

holes  in  flange,  91:4 

how  billed,  44:3 

how  shown,  39:1 

length,  86:6 

mill  variation,  22:2,  88:1 

ordered  length,  88:1 

ordering,  164:7 

properties,  table,  323 

seat  connection,  89:2 

shear  intensity,  202:1 

web  connection,  83:6 

weights,  tables,  300,  301 
CHANNEL  COLUMNS,  131:3,  132:1 
CHANNEL-COLUMN  SPLICES, 

132:1,  276:4 

CHANNEL  PURLINS,  90:1,  91:1 
CHECKERS,  20:4,  179:1,  180:2 
CHECKING  DRAWINGS, 

check  marks,  181 :2 

for  students,  182:2 

indicating  mistakes,  181:1 

suggestions,  180:3 

when  checked,  22:1,  179:2 
CHECK  MARKS,  181:2 
CHIEF  DRAFTSMAN,  20:4,  22:1 
CHIEF  ENGINEER,  20:2 
CHIPPING,  29:3,  30:4 
CHORD  MEMBERS,  form,   115:3, 

123:4 

CHUTES,  146:5 
CLAMP,  rail,  107:5,  317 
CLEARANCE,  73:4 

bridge,  130:4 

driving,  73:5 

erection,  73:1 

overrun  72:2 

where  provided,  72:1 
CLEARSTORY,  113:2 


CLEVIS,  174:2,  207:3 
CLOTH,  see  "tracing  cloth" 
CODE  OF  RIVETS,  304 
COLD  SAWS,  28:1 
COLLARS,  on  pins,  279:5 
COLLISION  STRUTS,  120:2 
COLUMN,  COLUMNS,  131:1 

anchor  bolts,  134:4 

arrangement  on  sheet,  131 :2 

bases,  134:4 

beam  connections,  132:3 

connections,  131:1,  134:3 

countersunk  rivets,  134:4 

crane,  134:2 

critical,  292:2 

dimensions,  132:1,  2,  134:6 

extension  figures,  134:6 

gable,  136:2 

gages, 

in  angles,  136:1,  3 
in  channels,  132:1 

girder  seats,  134:2 

latticed,  136:3 

loads,  292:2 

mill  building,  134:2 

milling,  134:5 

plate  and  angle,  131:3 

plate  and  channel,  131:3, 
132:1 

position  on  sheet,  131:2 

sectional  views,  134:1 

stiffening,  angles,  132:3 

types,  131:3 

use,  131:1 
COLUMN    BASES,    134:4,    174:3, 

290:1 

COLUMN  FORMULA,  211:2 
COLUMN  LOADS,  292:2 
COLUMN  SCHEDULE,  159:2,  161:1 
COLUMN  SPLICES,  132:1,   134:3, 

276:2,  3,  4 

COMBINATION    SHEETS,     173:2, 
174:2,3 


COMBINED    LOADS    on    beams, 

188:1,  192:2 

COMBINED  MEMBERS,  53:4,  81:3 
COMBINED  STRESSES,  axial  and 

bending,  215:1 

COMMERCIAL  LENGTHS,  114:2 
COMPASSES,  use,  57:2 
COMPONENTS,     diagrams,     312, 

313,  314 
COMPRESSION,      unit      stresses, 

'211:2 

COMPRESSION  FORMULA,  211:2 
COMPRESSION   FLANGES   of  gir- 
ders, 219:5 

COMPRESSION  MEMBERS,  206:2 
bending      and      compression, 

215:1 

cross  section,  206:3 
design,  211:1 

effect  of  rivet  holes,  206:4 
forms,  206:3,  212:2 
moment  of  inertia,  212:1 
radius  of  gyration,  211:3 
strength,  211:2 
thickness  of  metal,  212:2 
COMPUTATION,  arrangement, 

185:1,  208:3 
COMPUTERS,  170:1 
CONCENTRATED  LOADS, 
beams,  185:2 
cover  plates,  261:1,  2 
equivalent,  187:1 
flange  rivets,  243:2 
CONCRETE   MAT  under  grillage 

beams,  292:4 

CONNECTION,  CONNECTIONS, 
column,  132:3,  134:3 
eccentric,  see  "eccentric  con- 
nections" 
field,  50:5 

floor-beam,  rivets,  236:1 
independent,  232:2 
purlin,  119:1;  table,  315 


CONNECTION,  CONNECTIONS 
(Continued) 

riveted, 

assumptions,  228:4 
design,  229:1 

seat,  235:1 

skewed  beams,  94:5 

stringer,  rivets,  235:2 

web,  beams,  234:2 
CONNECTION  ANGLES,  83:6 

design,  86:3 

different  depths  of  beams,  86:2 

methods  of  detailing,  84:1,  2 

single  angle,  86:1 

tables,  298-302  incl. 
CONNECTION  PLATES, 

latticed  girder,  109:3,  112:1,2 

layout,  76:1,  77:1 
CONTINUOUS  BEAMS,  83:1,  192:4 
CONTINUOUS    RIVET    SPACING, 

70:4 
CONTINUOUS  STROKE  in  ruling, 

58:8 
CONTRACTING  DEPARTMENT, 

20:2 
CONVENTIONAL  METHODS, 

billing,  432 

representation,  38:3 
CONVENTIONAL  SIGNS, 

billing,  43:2 

different  materials,  42:1 
CONVENTIONAL  WHEEL  LOADS, 

193:1 

COOPERATION,   between  depart- 
ments, 22:3 
COOPER'S  ENGINE  LOADING, 

bending  moment,  195:1,  196:1 

floor-beam  reaction,  194:2 

shear,  193:2,  194:1 

table,  318 

through  girders,  196:2 

trusses,  196:3 
COORDINATES,  50:4 


342 


INDEX 


COPING,  29:3,  89:1 
CORED  HOLES,  174:3 
CORRECTIONS  on  drawings,  47:8, 

182:3 
CORRUGATED  STEEL,  114:2, 174:2 

diagrams,  152:6 
COTTER  PINS,  278:1 
COUNTERS,  120:2,  130:5 
COUNTERSUNK       RIVETS,       see 

"rivets" 

COURSE  OF  STUDY,  2:1 
COVER  ANGLES,  274:2 
COVER  PLATES, 
design,  219:3 
how  billed,  97:2 
length, 

algebraic     method,     259:4, 

263:1 

concentrated  loads,  261:1 
full  length,  97:2,  259:2 
graphical  method,  259:4 
moving  concentrated  loads, 

262:2 

theoretical,  259:3 
uniformly  distributed  loads, 

259:6 
variable  concentrated  loads, 

261:2 

net  area,  221:2,  222:2 
ordering  from  mill,  165:2 
rivets,  69:2 

developed  plate,  264:2 
flange  stress,  264:1 
points  considered,  263:3 
splice,  274:1 
thickness,  212:2 
use,  97:2,  259:1 
width,  219:3 
CRANES, 

locomotive,  20:1 
overhead,  27:4 

CRANE   CLEARANCE  DIAGRAMS, 
152:5 


CRANE  COLUMNS,  134:2 
CRANE  GIRDERS,  107:5 

cover  plates,  97:2 
CRANE  RUNWAY  BEAMS,  94:4 
CRANE  STOPS,  174:1 
CRIMPED  ANGLES,  29:4 

ordering,  165:1 

stiffeners,  97:1 
CRITICAL  COLUMN,  292:2 
CRITICAL  LOAD,  191:1,  195:1 
CRITICAL  RIVET,  237:3 
CROSS  BRACING,  138:5 

unsymmetrical,  141:1 
CROSS  FRAMES,  144:2 
CROSS  REFERENCES,  2:3 
CROSS  SECTION, 

area,  206:3 

eccentricity,  212:1 

of  a  hole,  208:2 
CROSS-SECTION  LINES,  37:2 
CURVED     ENDS    OF     GIRDERS, 

107:4,  274:3 

CURVED  SURFACES,  38:2 
CURVES, 

disregarded,  26:1,  38:2 

inking,  57:2,  59:5 
CUTS,    reentrant,    29:3,     123:6, 

141:4 

CUTTING  in  field,  72:1 
CYLINDRICAL  BEAMS, 

design,  200:1 

shear  intensity,  202:1 

DASHED  LINES,  37:1 

DATA  SHEETS,  151 :4 

DEAD  LOADS,  189:2 

DECIMAL    EQUIVALENTS,    table, 

333 

DECIMAL  SCALE,  35:3 
DECIMALS,  converting,  48:4 
DECK  BRIDGE,  120:2 
DEFINITIONS      of      engineering 

terms,  6-18  incl. 


DEFLECTION, 
beams,  203:2 
girders,  107:3 
trusses,  123:2 
DEPTHS, 

latticed  girders,  109:1 
plate  girders,  218:3 
effective,  224:1 
rivet  calculation,  242:3 
DERRICKS,  20:1,  27:3 
DESCRIPTION  of  tables,  334-338 

incl. 
DESCRIPTION  of   this  book,    1, 

2,  3 
DESIGN, 

beams,  see  "beams" 
bearing  plates,  288:2,  3 

double,  289:2 
column  splice,  276:2,  3,  4 
complete  structures,  206:1 
compression  members,  211:1 
eccentric  connections,  237:2,  3 
eye  bars,  207:5 
field  splices,  275:1 
flange  splices,  274:1,  2 
floor-beam  connections,  236:1 
grillage    beams,     293:1,  2,  3, 

294:1 

lattice  bars,  216:1,  3,  4 
pins,  see  "pins" 
plate  girders,  see  "plate  gir- 
ders" 

practical  points,  206:1 
reinforcing  plates,  284:3 
bearing,  284:4 
rivets,  285:1,  286:2 
tension  members,  286:1 
riveted  joints,  229:1 
riveted  tension  members,  see 

"tension  members" 
rods,  207:2,  3,  4 
splices,  see  "splices" 
stringer  connections,  235:2 


DESIGN  (Continued) 

tension  members,  see  "tension 
members" 

tie  rods,  201:3 

web  plates,  218:4 
DESIGNING  DEPARTMENT,   19:2, 

20:2 

DESIGN  SHEETS,  20:3 
DESIGNERS,  20:2,  3 
DETAILBRS,  180:1 
DEVELOPED  PLATE,  78:1,  264:2 
DIAGONAL     BRACING,     138:1,  5, 

145:1 

DIAGONAL  CUTS  in  beams,  94:5 
DIAGONALS,  diagrams  for  com- 
puting, 312,  313,  314 
DIAGRAMS,  151:1 

bearing  plates,  316 

corrugated  steel,  152:6 

crane  clearance,  152:5 

erection,  22:1,  151:1 

method  of  drawing,  157:1 

mill  buildings,  152:4 

office  buildings,  152:7,  157:1, 
159:1,  2 

plate-girder  bridges,  152:1 

resultants,  312,  313,  314 

rivet  spacing,  305,  306 

truss  bridges,  152:2 
DIAMETER  of  rivets  used  in  de- 
sign, 208:2,  230:1 
DIAPHRAGMS,  134:2 
DIE, 

punch,  29:5 

rivet,  30:4 
DIMENSION,  DIMENSIONS,  46:1,  2 

angles,  tables,  303 

avoid  ambiguity,  47:4 

Bethlehem  beams,  tables,  302 

bevels,  50:7 

bolts,  table,  304 

channels,  tables,  300,  301 

columns,  132:1,  2,  134:6 


DIMENSION,  DIMENSIONS  (Con- 
tinued) 

decimals  avoided,  48:4 

edge  distances,  49:4 

field  connections,  50:5 

figures,  see  below 

gages,  49:3 

girders,  95:3 

group  spacing,  49:7 

horizontal,  beams,  86:5 

how  determined,  46:4 

I-beams,  tables,  298,  299,  302 

importance,  46:2 

indicate  actual  measurements, 
46:3 

lattice  bars,  50:6 

latticed  girders,  109:2 

lines,  see  below 

not  given  to  edges  of  flanges, 
49:6 

not  repeated,  49:1 

only  one  method,  50:4 

plate  girders,  95:3 

polar  coordinates,  50:4 

position,  46:5 

rails,  table,  317 

rectangular  coordinates,  50:4 

recurring,  48:6 

reference,  106:6 

repeating,  49:1 

rivets,  table,  304 

shopmen   not   made   to   add, 
50:3 

slope,  50:7 

sum  of,  50:2 

supplementary  lines,  50:1 

units,  48:3 

vertical, 
beams,  84:2 
columns,  134:6 

when  recorded,  46:4 
DIMENSION  FIGURES, 

how  corrected,  47:8 


INDEX 


343 


DIMENSION  FIGURES  (Cont'd) 

how  made,  47:5,  48:2 

inking,  60:4 

method  of  writing,  48:5 

replaced  when  erased  by  mis- 
take, 63:7 

units,  48:3 

where  placed,  47:6 
DIMENSION  LINES, 

distance  apart,  47:3 

how  drawn,  47:1 

replaced  when  erased  by  mis- 
take, 63:7 

when  inked,  60:1 

where  placed,  47:2 
DIRECTION  MARKS,  82:4 
DISTANCE  between  views,  34:2 
DOLLY  BAR,  30:4 
DOT  AND  DASH  LINES,  37:1 
DOTTED  LINES,  37:1 
DOUBLE  LATTICED  GIRDERS, 

112:3 
DOUBLE  LATTICING,  50:6,  70:1, 

216:3 

DOUBLE  SHEAR,  230:2 
DRAFTING    DEPARTMENT,    19:3, 

20:4 

DRAFTING  FORMS,  35:4 
DRAFTSMAN,  19:1,  20:4 

checking  own  work,  36:4, 180:1 

use  of  diagrams,  151:2 
DRAWINGS, 

accuracy,  35:2 

appearance,  55:1 

arrangement,      34:3,      115:1, 
121:2,3,  131:2,  138:5 

back  checking,  182:1 

checking,  179:2 

conform  to  material  ordered, 
163:3 

corrections,  47:8,  182:3 

distance  between  views,  34:2 

elements,  33:2 


DRAWINGS  (Continued) 

how  made,  36:1 

in  book,  146:1,  see  preface 

indicating  mistakes,  181:1 

lines,  37:1 

making    in    ink    directly    on 
tracing  cloth,  65:1,  3 

methods   of  making,   36:1, 3, 
55:2 

parts  shown,  34:4 

planning,  66:2 

position  on  sheet,  34:3,  115:1, 
121:2,3,  131:2,  138:5 

procedure,  36:3 

projection,  33:3 

record,  159:3 

revisions,  182:4 

scales,  35:3 

sheet  numbers,  54:5 

size,  35:4 

structural,  33:1 

symmetrical,  34:5 

tracing,  see  "inking" 

views,  33:3,4,  34:1 

when  checked,  22:1 

when  made,  22:1 

working,  33:1 
DRILLING,  30:1 

in  field,  74:1 
DRILL  PRESS,  30:1 
DRIVING  CLEARANCE,  73:5 
DRIVING  NUTS,  278:1. 
DRYING  of  ink,  56:3,  59:6,  7,  8 
DULL  SIDE  of  tracing  cloth  used, 

55:4 
DUTIES, 

biller,  20:4 

checker,  20:4 

chief  draftsman,  22:1 

chief  engineer,  20:2 

detailer,  20:4 

draftsman,  20:4 

squad  foreman,  20:4,  22:1,  2 


EAVE  STRUTS,  138:3,  146:3 
ECCENTRIC  CONNECTIONS,  237:1 

center  of  gravity,  237:3,  238:1 

center  of  rotation,  237:3 

critical  rivet,  237:3 

eccentricity,  237:3 

method  of  designing,  237:2 

theory,  237:3 

working  rule,  238:1 
ECCENTRICITY,  212:1,  237:3 
ECONOMICAL  DEPTH  of  girders, 

218:3 
EDGE  DISTANCES,  69:3 

omitted,  49:4 

table,  305 

EDGE   OF   FLANGE   not   dimen- 
sioned, 49:6 
EDGED  PLATES,  165:2 
EFFECTIVE  DEPTH,  224:1 
EFFECT  OF, 

bending,  197:3 

rivet  holes,  201:1,  206:4 

spreading  of  rolls,  25:1 
ELASTIC  LIMIT,  197:3 
ELEVATION,  33:3 
END  STIFFENERS,  see  "stiffeners" 
END  VIEW,  34:1 
ENGINE  LOADING,  see  "Cooper's 

engine  loading" 
ENGINEERING  DEPARTMENT, 

20:2 

ENGINEERS'  S.CALE,  35:3 
EQUATIONS     OF     EQUILIBRIUM, 

183:2 

EQUILIBRIUM,  principles,  183:2 
EQUIVALENT  CONCENTRATED 

LOADS,  187:1 
ERADICATOR,  ink,  63:2 
ERASERS,  63:1 
ERASING, 

importance,  62:1 

object,  62:2 

secret,  62:5 


ERASING  (Continued) 

willingly,  62:3 
ERASING  SHIELD,  63:4 
ERECTION,  20:1 
ERECTION  BOLTS,  178:1 
ERECTION  CLEARANCE,  73:1 
ERECTION  CONSIDERATIONS,  74:1 
ERECTION  DIAGRAMS, 

corrugated  steel,  152:6 

girder  bridges,  152:1 

mill  buildings,  152:4 

office  buildings,  152:7,  159:1,  2 

truss  bridges,  152:2 

when  drawn,  22:1,  151:1 
ERECTION  MARKS,  see  "shipping 

marks" 
ERECTION  PLANS,  see  "erection 

diagrams" 

ERECTION  SEATS,  73:2 
ERECTOR'S  LIST  of  field  rivets 

and  bolts,  176:2 
ERECTOR'S  USE  OF  DIAGRAMS, 

151:3 
ESTIMATING  DEPARTMENT,  19:2, 

20:2 

ESTIMATOR,  20:3 
EXPANSION,  289:2 
EXTENSION  of  buildings,  119:4 
EXTENSION  FIGURES,  86:5,  134:6 
EXTERNAL  FORCES,  183:4 
EXTREME  FIBERS,  198:1 
EYE  BARS, 

design,  207:5 

how  billed,  45:1 

how  shown,  40:4,  150:1,  174:2 
EYE-BAR  SHOP,  27:3,  31:6 

FABRICATION,  27:1 
FACING,  31 :1 
FALSEWORK,  20:1 
FAN  TRUSS,  113:2 
FIBER,  extreme,  198:1 
FIBER  STRESSES,  197:3 


FIELD  CHECK,  179:2 
FIELD     CONNECTIONS,     dimen- 
sions, 50:5 

FIELD  CORRECTIONS,  74:1 
FIELD  RIVETS  AND  BOLTS,  see 

"rivets"  or  "bolts" 
FIELD  SPLICE,  girders,  275:1 
FIGURES, 

compressed,  48:1 

extension,  86:5,  134:6 

how  corrected,  47:8 

how  made,  47:5 

inking,  60:4 

method  of  writing,  47:5,  48:2 

replaced  when  erased  by  mis- 
take, 63:7 

where  placed,  47:6 
FILLERS, 

how  shown,  41 :3 

length,  96:4 

rivets,  232:1,  235:2 

size,  96:4 

FILLETS,  not  shown,  26:1 
FINE  LINES,  37:1 
FINISHING  ROLLS,  23:3 
FINK  TRUSS,  113:2 
FITTERS,  30:3 
FLANGES, 

beams,  holes,  201:1 

girders, 

center  of  gravity,  224:1 
composition,  219:1 
net  area,  221 :2 

no  dimension  to  edges,  49:6 
FLANGE  ANGLES,  96:2,  219:2 

gage,  106:3 

FLANGE     PLATES,     see     "cover 
plates" 

vertical,  227:1 
FLANGE  RIVETS,  241:1 

box  girders,  252:1 

cantilever  girders,  252:2 

cases,  243:1 


344 


INDEX 


FLANGE  RIVETS  (Continued) 
combined    static    web    loads, 

246:2 

complete  treatise,  241 :4 
concentrated  static  web  loads, 

bending  moment  theory, 
243:3 

how  applied,  243:2 

shear  theory,  244:1 
controlling  factors,  242:1 
depth  used,  242:3 
different  cases,  243:1 
flange  loads, 

bottom  flange,  249:2 

how  applied,  248:2 

theory,  249:1 
forces  considered,  242:2 
general  discussion,  241 :5 
general  rules,  106:1 
girders    with    four    angles    in 

each  flange,  253:1,  255:1 
girders  with  non-parallel 

flanges,  252:4 

girders    with    vertical    flange 
plates,  253:1,  2 

theory,  254:1,  2 

when  used,  253:1 
inclined  girders,  241 :3 
minimum  values,  table,  306 
moving  web  loads, 

approximate  method,  247:3 

how  applied,  247:1 

theory,  247:2 
pitch,  68:1,241:2 
resistance  of  web  considered, 

250:2 
strength  of  web, 

importance,  255:2 

minimum     pitches,     256:1; 
table,  306 

theory,  256:3 

unit  stresses,  256:2 
summary,  257 


FLANGE  RIVETS  (Continued) 

table  of  minimum  values,  306 

uniform  static  web  loads, 
how  applied,  244:2 
theory,  244:3 

variable  fixed  loads,  246:3 
FLANGE  SPLICES  in  girders,  see 

"splices" 

FLANGE  STRESSES  in  plate  gir- 
ders, 221:2 
FLATS,  165:2 
FLAT  ROOFS,  113:1 
FLATTENED  RIVETS, 

bridge  trusses,  130:2 

design,  231 :2 

how  shown,  40:6 
FLEXURE  FORMULA,  199:2 
FLOOR  BEAMS,  107:5 
FLOOR-BEAM  CONNECTIONS, 

rivets,  236:1 

FLOOR-BEAM  REACTION,  194:2 
FLOOR  GIRDERS,  107:5 
FLOOR  PIANS,   office   buildings, 

152:7,  157:1,  159:1 
FLOOR  PLATES,  146:4 
FLUX,  23:1 

FOOTINGS,  column,  291:1 
FOOT-POUNDS,  3:2 
FORCES, 

beams,  197:3 

centrifugal,  227:2 

external,  183:4 

girder  flanges,  242:2 

internal,  197:1 

lateral,  226:1 

pins,  278:3 

selection,  280:2 

plate  girders,  218:2 

signs,  6,  183:3 

sketches,  184:4 
FOREMAN,  squad,  20:4 
FORGE  SHOP,  27:3,  31:6 
FORCINGS,  174:1 


FORMS,  printed,  35:4 
FORMS  OF  MEMBERS, 

bridge  trusses,  123:4 

compression  members,  206:3, 
212:2 

roof  trusses,  115:3 
FORMULAS, 

compression  members,  211:2 

flexure,  199:2  ' 

shear   and   bending   moment, 
184:3 

use  of,  3:1 

FOUNDATION  PLANS,  152:1,  3 
FOUNDRY,  27:3,  31:6 
FRACTIONS,  47:7 
FRAMES,  cross,  144:2 
FRICTION  in  riveted  joints,  228:4 
FUTURE  EXTENSION,  119:4 

GABLE  COLUMNS,  136:2 
GAGES, 

angles,     68:5,     106:3,     132:3, 
136:1,  139:3;  table,  303 

beams,  tables,  298-302  incl. 

bracing  angles,  139:3 

channels,  tables,  300,  301 

columns,  132:1,  136:1 

dimensioned,  49:3 

flange  angles,  106:3 

I-beams,  tables,  298,  299,' 
302 

standard,  68:5,  106:3 

stiffening  angles,  106:3 
GAS  PIPE,  ordering,  166:1 
GAS-PIPE  SEPARATORS, 

beams,  91:5 

grillage,  292:1 

table,  316 
GIRDER,  GIRDERS, 

beam,  91:5 

box,  94:1,  107:2,  252:1 

cantilever,  in  foundations, 
292:4 


GIRDER,  GIRDERS  (Continued) 
crane,  107:5 

cover  plates,  97:2 
floor,  107:5 

latticed,  see  "latticed  girders" 
plate,  see  "plate  girders" 
stiffening,  112:6 
GIRDER  BEAMS,  Bethlehem, 

tables,  302,  324 

GIRDER  SEATS,  on  columns,  134:2 
GIRTS, 

gable,  119:5 
side,  146:2 

GORDON  FORMULA,  211:2 
GOVERNMENT  ANCHORS,  88:2 
GRAVITY,  CENTER  OF, 

compression  members,  212:1 
eccentric   connections,    237 :3, 

238:1 

girder  flanges,  224:1 
GRILLAGE  BEAMS, 
arrangement,  291:2 
bearing  pressure,  292:3 
concrete  mat,  292:4 
design, 

bending,  293:2 
buckling,  293:3 
method,  293:1 
shear,  294:1 

distance  between,  291 :2 
grouting,  291 :2 
loads,  292:2 

method  of  design,  293:1 
separators,  292:1 
stiffeners,  292:1 
tie  rods,  292:1 
when  used,  291 :1 
GROUP  DIMENSIONS,  49:7 
GROUT  between  grillage  beams, 

•   291:2 

GUARD,  scale,  35 
GUIDE  LINES  for  lettering, 
60:5 


GUSSET  PLATES, 
layout,  76:1 
rivets,  233:2,  3 
roof  trusses,  118:1 
symmetrical,  234:1 
GYRATION,  RADIUS  OF,  211:3 
tables, 

angles,  325,  326,  329 

Bethlehem  beams,  324 

channels,  323 

I-beams,  322 

two  angles,  329 

HAMMER,  pneumatic,  30:4 

HANDBOOKS,  1:1 

HAND  HOLES,  74:1 

HANGER,    center,    roof    trusses, 

118:3 
HEADS  of  shop  rivets,   weight, 

170:1 

HEAVY  LINES,  inking,  59:3 
HEEL  PLATES,  roof  trusses,  1 14 :3 
HINGED  SHOES,  289:3 
HIP  ROOF  CONSTRUCTION,  146:5 
HOLES, 

all  shown,  41:1 
anchors, 
beams,  88:2 
columns,  73:3 
girders,  73:3,  106:5 
areas,  table,  303 
boring,  31:2 
cored,  174:3 
cross  section,  208:2 
deducted    in    girder    flanges, 

221:2 

drilling,  30:1 
effect  of, 

beams,  201 :1 

tension     and     compression 

members,  206:4 
flanges  of  I-beams  and  chan- 
nels, 91 :4 


INDEX 


345 


HOLES  (Continued) 

how  billed,  45:6 

how  dimensioned,  49:2 

how  noted,  50:4 

how  shown,  40:6 

pin,  123:3 

punching,  29:5 

reaming,  30:2,  4 

sag  rods,  91 :1 

size,  30:4 

in  designing,  208:2 
in  drafting,  40:6 
how  noted,  52:4 

tie  rods,  90:2 

when  inked,  60:3 
HOOK  BOLTS,  317 
HOOKE'S  LAW,  197:3 
HOPPERS,  146:5 
HORIZONTAL  DIMENSIONS  in 

beams,  86:5 
HORIZONTAL  FLANGE  STRESS, 

242:2 
HOWE  TRUSS, 

bridges,  120:2 

roofs,  113:2 

I-beams, 

actual  shape,  26:1 
areas,  table,  322 
coping,  29:3,  89:1 
design,  200:2 
dimensions,  tables,  298,  299, 

302 

holes  in  flange,  91 :4 
how  billed,  44:2 
how  shown,  38:7 
length,  86:6 

mill  variation,  25:2,  88:1 
ordered  length,  88:1 
ordering,  164:7 
properties,  tables,  322,  324 
seat  corrections,  89:2 
shear  intensity,  202:1 


I-beams  (Continued) 
tie  rods,  90:2 
web  connections,  83:6 
weights,  tables,  298,  299,  302 
IDENTIFICATION  MARKS,  52:5 

see  also  "shipping  marks" 
IMPACT,  189:2 
INCLINED-CHORD  PRATT  TRUSS, 

120:2 
INDEPENDENT  CONNECTIONS, 

232:2 

INDICATING  MISTAKES  on  draw- 
ings, 181:1 

INDIRECT  RIVETING,  232:1 
INDIRECT  SPLICES,  274:2 
INERTIA,  MOMENT  OF,  212:1 
tables, 

angles,  325,  326 
Bethlehem  beams,  324 
channels,  323 
I-beams,  322,  324 
rectangles,  320 
INFORMATION  SHEETS,  20:3 
INGOTS,  23:3 
INGOT  MOLD,  23:3 
INITIAL  TENSION,  139:1 
INK, 

black,  36:2,  58:1 
drying,  56:3,  59:6,  7,  8 
frozen,  58:4 
never  diluted,  58:1 
not  shaken,  58:3 
red,  36:2,  58:1 
two  bottles,  58:1 
INK  ERADICATOR,  63 :2 
INK  ERASERS,  63:1 
INKING, 

continuous  strokes,  58:8 

curves,  57:2,  59:5 

directly    on     tracing     cloth, 

65:1,  3,  66:4 

draw  away  from  intersections, 
59:2 


INKING  (Continued) 
heavy  lines,  59:3 
method  of  procedure,  59:9,  10 
not  too  close  to  straight-edge, 

58:6 

parallel  lines,  59:4 
setting  of  pen,  58:9 
INSET  SHEETS,  1:2 
INSPECTION,  31 :3 
INSPECTOR,  31:3 
INTENSITY    OF    SHEAR,    beams, 

202:1 
INTERMEDIATE  STIFFENERS,   see 

"stiffeners" 
INTERPOLATION  of  rivet  values, 

231:1 
INTERSECTIONS,  draw  lines  away 

from,  59:2 
INTRODUCTORY,  1 
INVISIBLE  EDGES,  37:1 
IRON,  23:1 
IRON  ORE,  23:1 
ITEMIZING,  169:1 
ITEM  NUMBERS,  169:1 

JOINTS, 

bridge  trusses,  121:1 
riveted,  see  "connections" 

KNEE  BRACES,  141:2,  145:1 
KNIFE,  not   used   on   drawings 
63:3 

LATERAL  BRACING,  141 :3,  4 
LATERAL  FORCES,  226:1 
LATERAL  PLATES,  layout,  77:1 
LATERAL  SUPPORTS,  201 :2 
LATERAL  THRUST,  201:3 
LATTICE  BARS,   . 

design,  216:1,  3,  4 

how  billed,  45:2 

how  dimensioned,  50:6 

how  shown,  40:5 


LATTICE  BARS  (Continued) 

how  made,  45:2 

how  spaced,  70:1 

minimum  sizes,  216:3 

ordering,  166:1 

table,  315 

LATTICED  COLUMNS,  136:3 
LATTICED  GIRDERS,  108:1 

connection  plates,  109:3, 
112:1,2 

dimensions,  109:2 

double,  112:3 

end  connections,  108:3 

form,  108:2 

panel  depth  and  length,  109:1 

proportions,  108:4 

stiffening  girders,  112:6 

stitch  rivets,  112:4 

typical  connections,  112:5 

working  lines,  108:5 
LATTICED  TRUSSES,  108:1,  120:2 
LAYING  OUT,  29:2 
LAYOUT,  75:1 

bent  plates,  78:1 

gusset  plates,  76:1 

lateral  plates,  77:1 

plant,  27:4 

simple,  75:3 

types,  75:4 

when  used,  752 
LEAST  NET  SECTION,  209:1 
LEAST    RADIUS   OF    GYRATION, 

211:3 

LEFTS  and  rights,  81 :2 
LENGTHS, 

beams,  86:1 

cover     plates,      see      "cover 
plates" 

fillers,  96:4 

flange  angles,  96:2 

latticed  girders,  109:1 

multiple,  28:1 

ordered,  164:6 


LENGTHS  (Continued) 

plate  girders,  95:3 

stiffeners,  96:1 

trusses,  120:1 

web  plates,  96:2 
LETTERING,  use  of  guide  lines, 

60:5 

LETTERING  PEN,  57:3 
LIMITING  VALUE  OF  RIVETS, 

231:1 
LINE,  LINES, 

curved,  57:2,  59:5 

dimension,  see  "dimension 
lines" 

limiting,  75:3 

of  drawing,  37:1 

reference,  107:1 

replaced  when  erased  by  mis- 
take, 63:7 

when  inked,  59:10,  60:1,  2 
LISTS  OF  MATERIAL,  162:2 
LISTS  OF  MEMBERS,  60:5,  81:1 
LISTS  OF  RIVETS   AND   BOLTS, 

176:1,  2 
LIVE  LOADS,  189:2 

bending  moments,  see  "bend- 
ing moments" 

shear,  see  "shear" 
LOADS, 

column,  on  grillage,  292:2 

combined,  188:1,  192:2 

concentrated,  185:2,  3 

dead  or  static,  189:2 

live  or  moving,  189:2 

uniform,  187:1,  188:2 
LOCOMOTIVE  CRANE,  20:1 
LOCOMOTIVE  LOADING,  table, 

318 

LOMAS  NUTS,  278:1 
LONGITUDINAL  SHEAR  in  beams, 

202:1 

LOOP  RODS,  174:2,  207:2 
LOOSE  PIECES  bolted,  53:2 


346 


INDEX 


LOOSE  RIVETS,  31 :3 

LOUVRES,  119:6 

LUG,  118:1 

LUMBER,  commercial  lengths, 

114:2 
LUMP-SUM  CONTRACTS,  20:3 

MACHINE  SHOP,  27:3,  31:6 
MANUFACTURE  of  structural 

steel,  23:2 
MARKS, 

assembling,  79:2 
component  parts,  79 :4 
first  letter,  80:1 
second  letter,  80:2 
sheet  number,  80:3 
rights  and  lefts,  80:4 
summary,  80:5 
when  used,  79:3 
direction,  82:4 
shipping,  80:6 

bridge  trusses,  82:1,  123:1 
component  parts,  80:7 
list,  324 

marked  conspicuously,  81:1 
members  combined,  81:3 
office  buildings,  81 :5 
opposites,  81:4 
rights  and  lefts,  81 :2 
roof  trusses,  82:2 
tie  and  sag  rods,  82:3 
use,  52:5,  80:6 
MAT,  CONCRETE,  under  grillage 

beams,  292:4 
MATERIAL, 
conventional  representation, 

38:3,  42:1 

shipped  from  mill  to  site,  164:4 
when  billed,  60:5 
MATERIAL    ORDER    BILLS,    see 

"order  bills" 

MAXIMUM   BENDING   MOMENTS 
ON  PINS,  280:1 


MAXIMUM  RIVET  SPACING,  69:1 

table,  305 
MEMBERS, 
bridge  trusses,  123:4 
combined,  53:4,  81:3,  215:1 
compression,  see  "compression 

members" 
list  of,  60:5,  81:1 
number,  52:6 
pin-connected  trusses,   123 :3, 

284:2 

roof  trusses,  115:3 
tension,  see  "  tension  members ' ' 
METAL  SCRATCHER,  63:3 
METHODS  or 
billing,  43:1 
designing, 

eccentric  connections,  237:2 
pins,  278:2 
plate  girders,  220:1 
reinforcing  plates,  284:3 
dimensioning,  50:4 
drawing  section  lines,  37:2 
making  drawings,  36:1,  65:1,  3 
ordering  material,  162:3 
procedure, 

drafting  department,  22:1 
inking,  59:9,  10 
making  drawings,  36:3 
making  erection   diagrams, 

157:1 

making  layouts,  76:1,  77:1 
representation,  38:3 
MILL  BUILDINGS, 
bracing,  139:5 
column  bases,  134:4 
column  splices,  276:2 
columns,  134:2 
diagrams,  152:4 
MILL  ORDERS,  see  "order  bills" 
MILL  VARIATION,  25:2,  88:1 
MILLING,  31 :1 

bridge  members,  123:5 


MILLING  (Continued) 

columns,  134:5 
MILLING  MACHINES,  31:1 
MINIMUM  PITCH  of  flange  rivets, 

table,  306 
MINIMUM  RIVET  SPACING,  68:6; 

table,  305 

MINIMUM  RIVET  STAGGER,  dia- 
gram, 305 

MISCELLANEOUS  MATERIAL, 
drawing,  150:1,  174:1 
ordering,  163:1 
MISTAKES, 

correcting,  47:8 
guarding  against,  62:4 
indicating  on  drawing,  181 :1 
MODULUS,  SECTION,  199:1 
MOLD,  ingot,  23:3 
MOMENTS, 

bending,  see  "bending  mo- 
ments" 

of  inertia,  212:1 
plate  girders,  220:1 
tables, 

angles,  325.,  326 
Bethlehem  beams,  324 
channels,  323 
I-beams,  322 
rectangles,  320 
pins,  280:1;  table,  333 
point  of,  184:2 
resisting,  198:1 
signs,  6,  183:3 
three,  theorem,  192:4 
MOMENT  PLATES,  272:2 
MOMENT     TABLE,     for     engine 

loads,  318 
MONITOR,  113:2 

MOVING  LOADS,  see  "live  loads" 
MULTIPLE  LENGTHS,  28:1 
MULTIPLE  PUNCHES,  29:5,  91:2 
MULTIPLICATION  TABLE  for  rivet 
spacing,  307 


NAILING  STRIPS,  91:3 
NET  AREA, 

angles,  table,  327 

cover  plates,  221:2,  222:2 

ends  of  members,  210:2 

flange  angles,  221 :2 

flanges,  219:4 

least,  209:1 

plates,  208:2 

tension  members,  208:2 

two  angles,  table,  327 

working  rule,  210:1 
NET  SECTION,  see  "net  area" 
NEUTRAL  Axis,  197:3 
NEUTRAL  SURFACE,  197 :3 
NOMINAL  DIAMETER  of  rivets, 

230:1 

NOTATION,  3:2 
NOTES, 

general,  52:2 

made  positive,  53:5 

use,  52:1 

when  inked,  60:5 

where  placed,  52:2,  3 
NUMBER, 

holes   deducted    from    flange, 
221:2 

pieces,  52:6,  169:1 

rivets,  231:1 
NUMBERING, 

drawings,  54:5 

figures,  2:2 

order  bills,  164:2 

pages,  2:2 

paragraphs,  2:2 

sheets,  54:5 

shipping  bills,  171:1 

shop  bills,  167:2 
NUTS, 

driving,  278:1 

how  made,  31:6 

Lomas,  278:1 

pilot,  278:1 


NUTS  (Continued) 

pin,  278:1 
OFFICE  BUILDINGS, 

beams,  89:2 

bracing,  145:1 

column  bases,  174:3,  290:1 

column  schedules,  159:2 

column  splices,  132:1,  276:2,  4 

columns,  132:1 

diagrams,  152:7 

floor  plans,  152:7,  159:1 
method  of  procedure,  157:1 

shipping  marks,  81:5 
OGEE  (or  O.G.)  WASHERS,  174:1 
OPEN-HEARTH  STEEL,  23:2 
OPPOSITES,  81:4 
ORDER  BILLS, 

angles,  165:1 

arrangement,  163:4 

beams,  164:7 

changes,  164:5 

component  parts,  163:2 

drawings  must  conform,  163:3 

gas  pipe,  166:1 

lattice  bars,  166:1 

material  shipped  direct,  164:4 

methods,  162:2,  3 

mill  variation,  25:2,  88:1 

miscellaneous  material,  163:1 

numbering,  164:2 

ordered  lengths,  164:6 

plates,  165:2 

purpose,  162:1 

rails,  166:2 

sag  rods,  166:1 

shipments,  164:1 

specifications,  164:3 

tie  rods,  166:1 

ORDER  DEPARTMENT,  22:1, 162:2 
ORDERED  LENGTHS,  164:6 
ORDERING, 

angles,  165:1 

beams,  164:7 


INDEX 


347 


ORDERING  (Continued) 

gas  pipe,  166:1 

lattice  bars,  166:1 

plates,  165:2 

rails,  166:2 

tie  rods,  166:1 
ORGANIZATION   of    a    structural 

company,  19 

ORTHOGRAPHIC  projection,  33:3 
OUTLINE, 

course  of  study,  2:1 

this  book,  1,  2,  3 
OVERRUN,  72:2 

OXT-ACETYLENE     FLAME,    28:1, 
29:3,  89:1 

PACKING  on  pins,  279:5 

PAINTING,  31:4 

PAPER,    placed    under    tracing 

cloth,  66:3 

PARABOLA,  construction,  259:6 
PARALLEL  LINES,  inking,  59:4 
PART  I,  1 
PART  II,  1:1,  33 
PART  III,  1:1,  183 
PARTS  shown  on  drawings,  34:4 
PATTERNS,  31:6 
PATTERN  SHOP,  27:3,  31:6 
PEAK     PLATES,     roof     trusses, 

118:5,  234:1 

PEDESTALS,  cast-iron,  289:3 
PENS, 

lettering,  57:3 

ruling,  see  "ruling  pens" 
PEN  WIPERS,  56:3 
PENCIL  ERASERS,  63:1 
PENCIL    LINES    removed    from 

tracing  cloth,  64:1 
PERMANENT  BOLTS,  53:3 
PETTIT  TRUSS,  120:2 
PIECES, 

bolted,  53:2 

number,  52:6 


PIG  IRON,  23:1 
PILOT  NUTS,  278:1 
PINS, 

application  of  forces,  278:3 

bending,  279:1 

collars,  279:5 

components,  280:1 

computation,  280:3 

cotter,  278:1 

design,  278:2,  279:1 

forces,  278:3,  280:2 

investigation  for  shear,  279 :2 

maximum  bending  moments, 
280:1 

packing,  279:5 

resisting  moments,  table,  333 

selection  of  forces,  280:2 

shear,  279:2 

use,  278:1 

which  ones  designed,  279:4 
PIN-CONNECTED  TRUSSES,  types 

of  members,  284:2 
PIN  HOLES,  size,  123:3 
PIN  PLATES, 

design,  284:3,4,  286:1 

rivets,  285:1,  286:2 

when  used,  284:1 
PITCH   OF  FLANGE  RIVETS,   see 

"flange  rivets" 
PITCH  OP  ROOFS,  114:1 
PLAN,  PLANS,  33:3,  151:1 

anchor-bolt,  152:1,3 

erection,  151:1 

floor,  152:7 

method  of  drawing,  157:1 
PLANED  PLATES,  ordering,  165:2 
PLANING,  29:4,  31:1 
PLANT  LAYOUT,  27:4 
PLATE,  PLATES, 

area,  net,  208:2 

areas,  table,  321 

batten, 
size,  216:2 


PLATE,  PLATES  (Continued) 
batten  (Continued) 

use,  208:1,  212:2 
bearing,  see  "bearing  plates" 
bent, 

developed,  78:1 

how  billed,  43:3,  45:7 

how  shown,  41 :4 

layout,  78:1 
connection,  76:1,  77:1,  109:3, 

112:1,2 

cover,  see  "cover  plates" 
extreme  sizes,  25:3 
floor,  146:4 
gusset,  layout,  76:1 
how  billed,  43:3 
how  shown,  38:5 
lateral,  layout,  77:1 
net  area,  208:2 
ordering,  165:2 
pin, 

design,  284:3,4,  286:1 

rivets,  285:1,  286:2 

when  used,  284:1 
planing,  29:4 
reentrant  angles,  29:3 
reinforcing, 

bridges,  130:1 

design,  284:3,4,  286:1 
rivets,  285:1,  286:2 
when  used,  130:1,  284:1 

columns,  276:4 

girders,  266:3 
rolling,  25:3 
roof,  146:4 
sheared,  25:3 
shearing,  128:1 
splice,  270:2 

thickness,   compression  mem- 
ber, 212:2 
tie, 

size,  216:2 

use,  208:1,  212:2 


PLATE,  PLATES  (Continued) 

universal   mill    (U.M.),   25:3, 
165:2 

wall,  on  beams,  94:2 

web,  see  "web  plates" 

weights,  table,  321 
PLATE    AND    ANGLE   COLUMNS, 

131:3 
PLATE  AND  CHANNEL  COLUMNS, 

131:3,  132:1 
PLATE  GIRDERS, 

adaptability,  95:1 

area  of  flange,  219:4 

box,  107:2 

camber,  107:3 

centrifugal  forces,  227:2 

compression  flange,  219:5 

cover  plates,  see  "cover 
plates" 

crimped  stiffeners,  29:4,  97:1 

curved  ends,  107:4 

degree  of  accuracy  in  design- 
ing, 220:2 

depth,  95:3,  218:3 


Case  A  (resistance  of   web 

neglected), 
assumptions,  221:1 
flange  stress,  221 :2 
net  area, 

in  angles,  221 :2 

in  cover  plates,  221:2, 

222:2 

numbers    of     holes     de- 
ducted, 221:2 
theory,  221 :2 
Case  B  (resistance  of  web 

considered), 
additional  steps,  223:2 
assumptions,  223:1 
center  of  gravity  of  flange, 

224:1 
effective  depth,  224:1 


PLATE  GIRDERS  (Continued) 
design  (Continued) 
Case  B  (Continued) 
resistance  of  web,  223:3 
theory,  223:3 
Case  C  (moment  of  inertia), 

220:1 

compression  flange,  219:5 
degree  of  accuracy,  220:2 
depth,  218:3,  224:1 
distribution  of  area,  219:4 
end  stiffeners,  see  "stiffen- 
ers" 

flanges,  219:1 
forces,  218:2 
four  angles  in  each  flange, 

227:1 

impact,  225:1 
lateral  forces,  226:1 
methods,  220:1 
moment  of  inertia  method, 

220:1 

splices,  see  "splices" 
through  girders,  196:2 
vertical  flange  plates,  227:1 
web  plates,  218:4 
diagrams,  152:1 
fillers,  96:4 

flange  angles,  96:2,  219:2 
flange     rivets,     see     "flange 

rivets" 
flange     splices,     see     "flange 

splices" 

flanges,  composition,  219:1 
forces,  218:2 
four    angles    in    each    flange, 

227:1 

gages,  106:3 
horizontal,  218:1,  241:3 
impact,  225:1 
inclined,  241 :3 
lateral  forces,  226:1 
length,  95:3 


348 


INDEX 


PLATE  GIRDERS  (Continued) 
main  dimensions,  95:3 
methods  of  design,  220:1 
moment  of  inertia,  220:1 
net  area,  221:2,  222:1,  2 
resisting  moment,  218:2 
rivete, 

cover   plates,  106:2,  263:3, 

264:1,  2 

flange,  see  "flange  rivets" 
stiff eners,  96:3,  268:2,  269:4 
splices,  see  "splices" 
stiffeners,  see  "stiffeners" 
stresses,  221:1,2,  223:1 
thickness  of  web,  266:3 
types,  95:2 

vertical  flange  plates,  227:1 
web  plates,  96:2 
web  splices,  see  "splices" 
PLATE  SHEARS,  28:1 
PLATE  WORK,  146:4 
PLOTTING,  accuracy,  35:2 
PNEUMATIC  CHISEL,  29:3 
PNEUMATIC  HAMMER,  30:4 
PNEUMATIC  REAMER,  30:2,  4 
POCKET,  rain,  95:3 
POINT  OF  MOMENTS,  184:2 
POLAR  COORDINATES,  50:4 
PONY  TRUSSES,  144:1 
PORTAL  BRACING,  141:4,  145:1, 

146:5 
POSITION, 

of  dimensions,  46:5 

of    drawing    on    sheet,    34:3, 

115:1,  121:2,3,  131:2 
of  straight  edge,  58:5,  6 
of  title,  54:1 

POSTURE  when  inking,  58:7 
POUND-FEET,  3:2 
POUND-INCHES,  32 
POUND  PRICE,  20:3,  170:1 
POWDER,  for  tracing  cloth, 
56:2 


PRACTICAL    POINTS    in    design, 

206:1 
PRATT  TRUSSES, 

bridges,  120:2 

roofs,  1132 

PRELIMINARY  SKETCH,  35:1 
PRINTED  FORMS,  35:4,  174:1,  2 
PROCEDURE,  method  of, 

drafting  room,  22:1 

inking,  59:9,  10 

making  drawings,  36:3 

making  layouts,  76:1,  77:1 
PROGRESS  RECORDS,  22 :2 

beams,  159:4 

columns,  161:1 
PROJECTING  PARTS,  72:4 
PROJECTION,  33:3 
PROJECTION  LINES,  37:1,  47:1 
PROPERTIES,  tables, 

angles,  325,  326 

Bethlehem  beams,  324 

channels,  323 

I-beams,  322 

rails,  317 

rectangular  beams,  319 
PROTECTION    OF    JOINTS    from 

weather,  130:3 
PROVISION  for  overrun,  72:2 
PUMICE  STONE,  56:2 
PUNCH,  29:5 

center,  27:5,  29:2 

multiple,  29:5,  91:2 
PUNCH  DIE,  29:5 
PUNCHING,  29:5 
PURLINS,  90:1 

holes  for  sag  rods,  91:1 

ordering,  164:7 

spacing,  114:2 

PURLIN     CONNECTIONS,      90:1, 
119:1;  table,  315 

RACK,  spacing,  29:5 
RADIAL  DRILL,  30:1 


RADIUS  OF  GYRATION,  211:3 

tables, 

angles,  325,  326,  329 
Bethlehem  beams,  324 
channels,  323 
I-beams,  322 
two  angles,  329 
RAIL  CLAMPS,  174:1 
RAIL  FASTENINGS,  317 
RAIL  SPLICES,  table,  317 
RAILS, 

how  billed,  44:7 

how  shown,  40:3,  174:2 

ordering,  166:2 

properties,  table,  317 
RAIN  POCKETS,  95:3 
RANKINE  FORMULA,  211:2 
RATIO  OF  SLENDERNESS,  211:2 
REACTIONS, 

concentrated  loads,  185:2 

floor-beam,  194:2 

forces  considered,  183:4 

sketches,  184:4 

symmetrical,  185:2 
REAMING,  30:1,  4 
RECEIVING  YARD,  28:1 
RECORD, 

drawings,  159:3 

progress,  159:4,  161:1 
RECTANGULAR  BEAMS, 

design,  199:2 

moment  of  inertia,  table,  320 

properties,  table,  319 

shear  intensity,  202:1 
RECTANGULAR  COORDINATES, 

50:4 

RECURRING  DIMENSIONS,  48:6 
RED  INK,  36:2,  58:2 
REDUCTION  of  iron  ore,  23:1 
REDUCTION  FORMULA,  211:2 
REENTRANT  ANGLES,  29 :3, 123 :6, 

141:4 
REFERENCE  DIMENSIONS,  106:6 


REFERENCE  LINES,  107:1 
REFERENCES, 
cross,  2:3 

to  other  drawings,  53:1 
REINFORCED   CONCRETE   FOOT- 
INGS, 291:1 
REINFORCING  PLATES, 
bridges,  130:1 
design,  284:3 
bearing,  284:4 
tension,  286:1 
rivets,  285:1,  286:2 
columns,  276:4 
when  used,  130:1,  284:1 
REPRESENTATION,  conventional, 

38:3 

REQUIRED  LISTS,  81:1 
RESISTANCE  of  web  plate,  223:3 
RESISTING  MOMENTS, 
beams,  198:1 
girders,  218:2 
pins,  table,  333 
RESTRAINED  BEAMS,  192:4 
RESULTANTS,  diagrams,  312,  313, 

314 

REVISIONS  of  drawings,  182 :4 
RIDGE  STRUTS,  118:5 
RIGHTS  AND  LEFTS,  81 :2 
RIVETS,  228:1 

assumptions  in  design,  228:4 

axial  tension,  228:4 

beam  connections,  234:2, 235:1 

bearing,  230:3 

bearing  values,  tables,  308-31 1 

incl. 

bending,  228:4 
code,  304 
countersunk, 

bridge  trusses,  130:2 
column  bases,  134:4 
driving,  30:4 
how  shown,  40:6 
value,  231:2 


RIVETS  (Continued) 
cover  plates, 

developed  plate,  264:2 

flange  stress,  264:1 

points  considered ,  106 :2, 263 :3 
critical,  237:3 
design,  229:1 
diameter,  nominal,  230:1 
distribution  of  stress,  228 :4 
double  shear,  230:2 
double-shear    values,    tables, 

308-311  incl. 
driving,  30:4 
driving  clearance,  73 :5;   table, 

304 
eccentric      connections,      see 

"eccentric  connections" 
edge  distance,  .69:3;  table,  305 
field,  228:2 

erector's  lists,  176:2 

grip,  176:2 

length,  176:2 

number,  177:1 

summary,  177:1 
fillers,  232:1,  235:2 
flange,  see  "flange  rivets" 
flattened,  40:6,  130:2,  231:2 
floor-beam  connections,  236:1 
gages,  68:5,  106:3 
gusset  plates,  233:2,  3 
heads, 

shape,  30:4 

table,  304 

weight,  170:1 
holes,  see  "holes" 
how  billed,  45:4 
how  dimensioned,  49:2 
how  made,  31:6 
.  how  shown,  40:6 
indirect,  232:1 
inspection,  31:3 
limiting  value,  231:1 
list,  176:1,  2 


INDEX 


349 


RIVETS  (Continued) 
loose,  31:3 

maximum  spacing,  table,  305 
minimum  spacing,  tables,  305, 

306 
minimum    stagger,    diagram, 

305 

more  than  one  used,  228:1 
nominal  diameter  used  in  de- 
sign, 230:1 
noting  size,  52:4 
number,  231:1 
pitch,  68:1 

position  in  member,  228:3 
reinforcing  plates,  285:1,  286:2 
shank,  30:4 
shear,  230:2 
shop,  30:4,  228:2 
single  shear,  230:2 
single-shear     values,    ;tables, 

308-311  incl. 
spacing,  68:1 

continuous,  70:4 

cover  plates,  69:2 

maximum,  69:1,  table  305 

minimum,  68:6,  table  305 

multiplication  table,  307 

practical  points,  702 

rules,  68:2 

stitch,  69:4 

subdivisions,  50:2 

uninterrupted,  49:5 

usual,  70:3;   table,  305 
splice  plates,  see  "splices" 
staggered,  49:2 
stiffeners,  96:3,  268:2,  269:4 
stitch,  69:4,  112:4,  118:2 
strength, 

in  bearing,  230:3 

in  shear,  230:2 
stringer  connections,  2352 
unit  stresses,  230:2,  3 
use,  228:1 


RIVETS  (Continued) 

values,  tables,  308-311  incl. 

weight,  170:1 

when  inked,  60:3 
RIVET  LINES,  37:1,  49:2 
RIVETED  JOINTS,  design,  229:1 
RIVETED    TENSION     MEMBERS, 

see  "tension  members" 
RIVETERS,  30:4,  60:3 
RIVETING,  30:4 
ROCKERS,  289:3 
RODS, 

bracing,  119:2 

design,  207:2,3,  4 

drawing,  150:1,  174:1,  174:2,  4 

how  billed,  44:4 

how  shown,  392 

lengths,  174:4 

marking,  174:4 

sag,  166:1,  174:4 

tables,  315 

tie,  166:1,  174:4 
ROD  CONNECTIONS,  316 
ROLLERS,  174:1,  289:3 
ROLLING  STEEL,  23:3 
ROLLS, 

effect  of  spreading,  25:1 

finishing,  23:3 

roughing,  23:3 

straightening,  29:1 
ROOF  PLATES,  146:4 
ROOP  TRUSSES, 

arrangement  on  sheet,  115:1 

bottom-chord  bracing,  119:3 

camber,  113:2 

center  hanger,  118:3 

flat,  113:1 

form  of  members,  115:3 

future  extension,  119:4 

gable  girts,  119:5 

gusset  plates,  118:1 

heel  plates,  1143 

louvres,  119:6 


ROOF  TRUSSES  (Continued) 

peak  plates,  118:5,  234:1 

pitch,  114:1 

purlin  connections,  119:1 

purlin  spacing,  114:2 

ridge  strut,  118:5 

rod  connections,  119:2 

saw  tooth,  1132 

scale,  1152 

sections  for  shipment,  118:4 

shipping  marks,  82:2 

stitch  rivete,  118:2 

supports,  114:3 

types,  1132 

use,  113:1 

working  lines,  115:2 
ROOT  AREAS,  207:4,  table,  315 
ROTARY  PLANER,  31 :1 
ROTATION,  center  of,  237:3 
ROUGHING  ROLLS,  23:3 
RULE, 

bending     moment,    short-cut, 
188:2 

eccentric  connections,  238:1 

net  section,  210:1 

rivet  spacing,  68:2 
RULING  PENS, 

care,  56:3,  57:1 

cleaning,  56:3 

filling,  56:3,  58:8 

lettering  with,  57:3 

setting,  58:9 

sharpening,  57:1 

stopping,  58:7,  59:1 

use,  56:3 
RUNWAY  BEAMS,  ordering,  164:7 

SAFE  LOADS, 

angles,  tables,  330,  331 
compression  members,  211:2 

SAG  BARS,  146:2 

SAG  RODS,  146:2 
drawing,  174:4 


SAG  RODS  (Continued) 

holes,  91:1 

marking,  174:4 

ordering,  166:1 

spacing  in  purlins,  91:1 

table,  316 
SAWS,  cold,  28:1 
SAW-TOOTH  TRUSS,  1132 
SCALE, 

of  drawing,  35:3 

bracing  systems,  138:5 
roof  trusses,  115:2 

use,  35:3 

SCALE  GUARD,  35:3 
SCHEDULE,  column,  159:2,  161:1 
SCOPE  of  this  book,  1 :1 
SCRATCHER,  avoid  use,  63:3 
SEAT,  erection,  73:2 
SEAT  CONNECTION, 

beams,  732 

design,  235:1 

girders,  134:2 

independent,  232:2 
SECTION, 

for  shear,  184:1 

least  net,  209:1 

net,  at  ends  of  tension  mem- 
bers, 210:2 

roof  trusses,  118:4 
SECTION  LINES,  37:2 
SECTION  MODULUS,  199:1 

tables, 

angles,  325,  326 
Bethlehem  beams,  324 
channels,  323 
I-beams,  322 
rectangular  beams,  319 
SECTIONAL  VIEWS,  37:1,  134:1 
SEGMENT  of  beam,  183:4,  184:4 
SELVAGE  EDGES,  55:5 
SEPARATORS, 

beams,  91:5,  174:1 

grillage,  292:1 


SEPARATORS  (Continued) 

table,  316 

SETTING  of  pen,  58:9 
SHADE  LINES,  38:2 
SHANK,  rivet,  30:4 
SHAPE  of  cross  section,  26:1 
SHAPES  most  used,  38:4 
SHARPENING  ruling  pen,  56:3 
SHEAR,  183:1 

arrangement  of  computation, 
185:1 

combined  loads,  188:1 

concentrated  loads,  186:1 

Cooper's  engine  loading, 

193:1,2,  194:1;  table,  318 

definition,  184:1 

design  for, 

beams,  292:1,  294:1 
girders,  218:2 

double,  230:2 

forces  considered,  183:4 

formulas,  184:3 

intensity,  202:1 

longitudinal,  202:1 

live-load,  cantilever  beams, 
190:1 

live-load,  simple  beams,  189:3 

pins,  2792 

principles,  183:2 

reactions,  185:2,  194:2 

relation  to  bending  moment, 
189:1 

rivets,  2302 

signs,  6,  183:3 

single,  2302 

sketches,  184:4 

uniform  loads,  187:1 

values   for   rivets   and   bolts, 

tables,  308-311  incl. 
SHEARED  PLATES,  25:3,  1652 
SHEARING,  28:1 
SHEARING  STRESSES  in  web, 
266:1 


350 


INDEX 


SHEARS,  28:1 

SHEET  NUMBERS,  54:5 
assembling  marks,  80:3 

SHIELD,  erasing,  63:4 

SHIPMENTS,  order  bills,  164:1 

SHIPPING,  31:5,  118:4 

SHIPPING  BILLS,  171:1 
when  made,  22:1 

SHIPPING  MARKS,  80:6 
bridge  trusses,  82:1,  123:1 
component  parts,  80:7 
list,  324 

marked  conspicuously,  81:1 
members  combined,  81:3 
office  buildings,  81  :5 
opposites,  81:4 
rights  and  lefts,  81  :2 
roof  trusses,  82:2 
tie  and  sag  rods,  82:3 
use,  52:5,  80:6 

SHOES,  bridge,  289:3 

SHOP  BILLS, 

arrangement,  167:4 
bolts  for  shipment,  167:4 
calculated  weights,  170:1 
component  parts,  167:3 
form,  167:2 
itemizing,  169:1 
notes,  167:4 
numtftftig,,  167:2 


weights  of  rivet  h&idfef  170:1 
when  made,  22  a  OSS  ,aia 

SHOP 

combined  wit 

SHOP  METHODIC: 

SHOP  Rivfci*lIs<!*b»t>K««&rtinu 


II8-80S  ,89ld,&t 


of  forces  and  ihetoh 

.dS'KJStSeaaeaflTS  OHIHA3H8 

SIMPLE  BEAMS,  83:11:992 


SINGLE  PUNCH,  29:5 
SINGLE  SHEAR,  230:2 
SINGLE  LATTICING,  70:1 
SIZE,  46:1 

bearing  plates,  288:2 
drawing,  35:4 
holes,  noting,  52:4 
pin  holes,  123:3 
rivet  holes,  30:4 
SKETCHES, 
forces,  184:4 
members,  35:1 

SKETCH  PLATES,  ordering,  165:2 
SKEWS  ACK  ANGLES,  94:3 
SKEWBACKS,  94:3,  316 
SKEW  CONNECTIONS  for  beams, 

94:5 

SKEW  PORTALS,  146:5 
SKEW  WORK,  146:5 
SLAG,  23:1 

SLENDERNESS  RATIO,  211:2 
SLOPE, 

calculation,  762 
how  dimensioned,  50:7 
roof,  114:1 
SOAKING  PITS,  23:3 
SOAPSTONE,  29:2 
SOIL,  bearing,  292:3 
SPACING, 

lattice  bars,  70:1 
purlins,  114:2 
rivets,  68:1 

continuous,  70:4 
cover  plates,  69:2 
flange,  see  "flange  rivets" 
maximum,  69:1;  table,  305 
Minimum,  68:6;  table,  305 
^Multiplication  table,  307 
points,  70:2 


stiff  eners,  96:3,  268:2,  269:4 
usual,  101(31 
SPACING  RACK,  E&5 


SPECIFICATIONS,  68:4,  164:3 
SPIKING  PIECES,  91:3 
SPLICE,  SPLICES,  270:1 
bridge  members,  123:6 
columns,  276:2,  3,  4 
design,  270:2 
girders, 
field,  275:1 
flange, 

angles,  274:2 
cover  plates,  274:1 
curved  ends,  274:3 
when  used,  273:2 
where  placed,  273:2 
web, 

design,  270:5 

moment,  272:1,2 
shear,  271:1,  272:2 
when  used,  270:4 
where  placed,  270:4 
indirect,  274:2 
rails,  317 
types,  270:3 
use,  270:1 

SPLICE  ANGLES,  274:2 
SPLICE  PLATES,  270:2 
SPONGE  ERASER,  56:2,  64:1 
SQUAD,  20:4 
SQUAD  FOREMAN,  20:4 
SQUARES,  table,  332 
STAGGERED  RIVETS, 
how  dimensioned,  49:2 
minimum,  diagram,  305;  table, 

306 
STANDARD  BEARING  PLATES, 

table,  316 
STANDARD  CONNECTION  ANGLES, 

tables,  298-302  incl. 
STANDARD  GAGES,  68:5,   132:1, 

136:1 
tables, 

angles,  303 
channels,  300,  301 


STANDARD  GAGES  (Continued) 
tables  (Continued) 

I-beams,  298,  299,  302 
STANDARDS, 

rails,  44:7,  68:3 
STATIC  LOADS,  189:2 
STEEL, 

manufacture,  23:2 
ruling,  23:3 

unit  stresses,  table,  317 
STIFFENERS,  or  STIFFENING 

ANGLES, 

columns,  132:3,  134:2 
cutting,  29:4 
girders, 
end,  266:4 

design  for  bearing,  267:1 
gages,  106:3 
length,  96:1 
position,  266:2 
rivets,  268:2 
strength     in     compression, 

268:1 
intermediate, 

crimping,  29:4  97:1,  269:5 
rivets,  96:3,  269:4 
spacing,  269:3 
when  used,  269:2 
grillage  beams,  292:1 
ordering,  165:1 
outstanding  legs  in  contact, 

106:4 

STIFFENING  GIRDERS,  112:6 
STITCH  RIVETS,  69:4, 112:4, 118:2 

spacing,  69:4 
STOCK  YARD,  28:1 
STOVE,  23:1 

STRAIGHT-EDGE  position,  58:5,  6 
STRAIGHTENING  ROLLS,  29:1 
STRAIGHT-LINE  FORMULA,  211:2 
STRAIN,  197:3 
STRENGTH  OF, 

compression  members,  211:2 


STRENGTH  OF  (Continued) 

countersunk  rivets,  231:2 

flattened  rivets,  231 :2 

rivets  in  bearing,  230:3 

rivets  in  shear,  230:2 

single  angles  in  compression, 
table,  330 

two    angles    in    compression, 
table,  331 

two  angles  in  tension,  table, 
327 

web  plates,  255:2 
STRESSES, 

combined  bending  and  axial, 
215:1 

compressive,  197:3 

flange,  221:2 

horizontal,  221:2 

plate  girders,  221:1,  2,  223:1 

tensile,  197:3 

unit,  see  "unit  stress" 

vertical,  248:2 
STRESS  SHEETS,  20:3 
STRINGER  CONNECTION,  design, 

235:2 
STROKE,   continuous,  in  inking, 

58:8 

STRUCTURAL  DRAFTSMAN,  19:1 
STRUCTURAL  DRAWINGS,  33:1 

appearance,  55:1 

elements,  33:7 

method  of  making,  36:1, 65:1,3 
STRUCTURAL  SHAPES,  38:4 
STRUCTURAL  SHOP,  19:5 
STRUCTURAL  STEEL,  23:2 
STRUTS, 

bracing  systems,  138:3 

collision,  120:2 

eave,  138:3,  146:3 

portal,  141:4 

ridge,  118:5 

top,  141:4 
STUB  PENS,  57:3 


INDEX 


351 


STUDENTS'  DRAWINGS,  checking, 

182:2 

SUBDIVISIONS,  rivet  spacing,  50:2 
SUB-PRATT  TRUSS,  120:2 
SUB-PUNCHING,  30:2 
SUM  of  dimensions,  50:2 
SUMMARY, 

assembling  marks,  80:5 
field  rivets  and  bolts,  177:1 
flange  rivet  spacing,  257 
SUPPLEMENTARY  DIMENSION 

LINES,  50:1 

SURFACE  OP  TRACING  CLOTH, 
prepared,  56:2 
restored,  63:6 
SWAY  BRACING,  141:4 
SWEDGE  BOLTS,  152:3,  316 
SYMMETRICAL    GUSSET    PLATE, 

234:1 

SYMMETRICAL  LOADS,  185:2 
SYMMETRICAL  MEMBERS,  34:5  ' 
SYSTEMS  of  bracing,  138:1,  2,  3 

T,  or  TEE, 

how  billed,  44:5 

how  shown,  40:1 
TABLES, 

arrangement,  1:1 

description,  334-338  incl. 
TACKS,  56:1 
TANK  WORK,  146:4 
TEMPLETS,  27:5 
TEMPLET  SHOP,  19:4,  27:5 
TENSILE     STRENGTH     of     two 

angles,  table,  327 
TENSION, 

initial,  139:1 

on  rivets,  228:4 
TENSION  MEMBERS, 

cross  section,  206:3,  208:2 

design,  206:2,  207:1 

effect  of  rivet  holes,  206:4 

eye  bars,  207:5 


TENSION  MEMBERS  (Continued) 
reinforcing  plates,  286:1 
riveted, 

bending  and  tension,  215:1 
design,  208:4 
net  area,  208:2 
at  ends,  210:2 
least,  209:1 
working  rule,  210:1 
size  of  rivet  holes,  208 :2 
rods,  207:2,3,4 
TESTS  for  students,  182:2 
THEOREM  of  three  moments, 

192:4 
THICKNESS, 

bearing  plates,  288:3 

girder  webs,  266:3 

metal,  compression  members, 

212:2 

THROUGH  BRIDGE,  120:2,  152:1 
THROUGH  GIRDERS,  bending 

moment,  196:2 
TIES,  cut  for  curves,  97:2 
TIE  PLATES, 
size,  216:2 
use,  208:1,  212:2 
TIE  RODS, 
design,  201 :3 
drawing,  174:4 
grillage  beams,  292:1 
holes,  90:2 
marks,  82:3,  174:4 
ordering,  166:1 
spacing,  90:2 
table,  316 
TIGHT  FITS,  72:3 
TIMBER,  unit  stresses,  table, 

320 
TITLE, 

component  parts,  54:2,  3 
smaller  drawings,  54:4 
when  inked,  61 :1 
where  placed,  54:1 


TOP  ANGLES,  89:2,  132:3 
TOP  LATERAL  BRACING,  141:4 
TOP  VIEW,  34:1 
TRACERS,  36:1,  65:2 
TRACING,  see  "inking" 
TRACING    inverted    when    com- 
pleted, 61:2 
TRACING  CLOTH, 

care  of,  55:3 

drawing   directly   in   ink   on, 
65:1,3,66:4 

dull  side  used,  55:4 

preparation  of  surface,  56:2 

selvage  edges  removed,  55:5 

stretching,  56:1 

surface  restored,  63:6 
TRACING  CLOTH  POWDER,  56:2 
TRACK,  225:1 
TRAVELERS,  20:1 
TRUSSES, 

bridge  trusses,  see  "bridge 
trusses" 

roof  trusses,  see  "roof  trusses" 
TYPE  used  in  this  book,  2:4 
TYPES  OP, 

bearing  plates,  288:1 

columns,  131:3 

latticed  girders,  108:2 

layout,  75:4 

members, 

bridges,  123:4 
roof  trusses,  115:3 

plate  girders,  95:2 

trusses, 

bridges,  120:2 
roofs,  113:2 

UNIFORMLY  DISTRIBUTED  LOADS, 
bending  moment,  187:1,  188:2 
cover  plates,  259:6 
flange  rivets,  244:2,3 
short-cut    rule    for    bending 
moment,  188:2 


UNITS, 

bending  moments,  3:2,  184:2 

design  of  beams,  199:2 

working,  34:6 
UNIT  STRESS, 

bearing,  230:3 

bending,  198:2 

bolts,  230:4 

compression,  211:2 

rivets,  230:2,  3 

shear,  230:2 

steel,  table,  317 

wood,  table,  320 
UNIVERSAL  MILL  (U.M.) 
PLATES,  25:3 

ordering,  165:2 

use  in  girders,  97:2 
UNSYMMETRICAL  BRACING,  141:1 
UNSYMMETRICAL  MEMBERS, 

212:1 

U-PLATES,  316 
UPSET  RIVETS,  30:4 
UPSET  RODS,  207:4;  table,  315 

VALLEY  ROOF  CONSTRUCTION, 

146:5 
VALUES  OF  RIVETS, 

bearing,  230:3 

interpolation,  231:1 

limiting,  231 :1 

shear,  230:2 

tables,  308-311  incl. 
VARIATION,  mill,  25:2,  88:1 
VERTICAL  FLANGE  PLATES,  227:1 
VERTICAL  FLANGE  STRESS,  248:2 
VIEWS,  33:3,  4,  34:1,  121:3 

distance  between,  34:2 

sectional,  37:2,  134:1 
VISIBLE  EDGES,  37:1 

WALL  PLATES  on  beams,  94:2 
WARREN  TRUSS,  108:2,  120:2 


WASHERS, 
beveled,  174:1 
how  billed,  45:3 
how  shown,  41 :3 
O.G.,  174:1 
WEB  CONNECTIONS  for  beams, 

83:6,  234:2 

WEB  PLATES  or  WEBS, 
beams,  202:1,  293:3 
compression  members,  thick- 
ness, 2122 
plate  girders,  96:2 
design,  218:4 
length,  96:2 
resistance,  223:3 
shearing  stresses,  266:1 
splice,  see  below 
thickness,  266:3 
weights,  table,  321, 
WEB  SPLICES, 
design,  270:5 

moment,  272:1,  2 
shear,  271:1,  272:2 
when  used,  270:2,  4 
where  placed,  270:4 
WEB  STIFFENERS,   see  "  stiff en- 

ers" 
WEIGHTS, 

beams,  assumed,  200:3 
calculated,  170:1 
tables, 
angles,  303 

Bethlehem  beams,  302 
bolts,  304 
channels,  300,  301 
I-beams,  298,  299,  302 
plates,  321 
rails,  317 
rivets,  304 
rods,  315 

WHEEL,  critical,  191:1,  195:1 
WHEEL-LOAD  SYSTEMS,  193:1 
WIDE  LINES,  inking,  59:3 


352 


INDEX 


WIKTHS  of  cover  plates, 

219:3 

WIND  BRACING,  138:1,  145:1 
WOOD, 

unit  stresses,  table,  320 

weight,  200:3 


WOODEN  BEAMS, 
actual  sizes,  199:3 
design,  199:3 
properties,  table,  319 
shear  intensity,  202:1 

WORKING  DRAWINGS,  33:1 


WORKING  LINES,  37:1 
bracing,  138:4,  5 
layouts,  76:1,2,  77:1 
trusses, 

bridge,  121:3 
roof,  115:2 


WORKING  RULE, 

eccentric  connections,  238:1 

net  section,  210:1 
WORKING  UNITS,  34:6 

YARD,  receiving  or  stock,  28:1 


Z-BARS, 

how  billed,  44 :6 
how  shown,  40:2 


AND     TO     s     00     ON        HE 
OVERDUE.  HE     SEVENTH     DAY 


YD 


TJ55 

J-?  O 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


